Institute of Fundamental Technological Research

This paper introduces MorphoGen — an integrated reliability-based topology optimization and nonlinear finite element analysis system for 2D and 3D domains. The system’s key innovation is its seamless prototyping of scientific formulations for computational problems in topology optimization. Its layered and object-oriented architecture, based on the template method design pattern, facilitates effortless modifications of algorithms and the introduction of new types of finite elements, materials, and analyses. MorphoGen also offers flexible handling of objective functions and constraints during topological optimization, enhancing its adaptability. It empowers researchers and practitioners to explore a wide range of engineering challenges, fostering a deeper understanding of complex structural behaviors and efficient design solutions. There are many topology optimization software and open source codes, especially based on the classical SIMP method. Unlike these codes our package is freely distributed among users and since it is distributed on the MIT licence, which allows for its easy modification depending on the particular needs of the users. For this purpose, we use the topology optimization algorithm proposed for the first time in our previous paper (Blachowski et al., 2020). The algorithm is based on a fully stress design-based optimality criteria and can be applied for topology optimization of either linearly elastic and elastoplastic structures. Additionally, the novelty of the proposed system is related to its ability of solving optimal topology under various constraints such as displacement, stresses and fatigue in both deterministic and probabilistic cases. Another application are modular structures, which reduce design complexity and manufacturing costs as well as rapid reconfiguration. However, in the realm of structural optimization, modular systems are more challenging due to various: modes of operation of the modules and the stresses configurations. Moreover, this area of research is dramatically less explored. Thus the effectiveness of MorphoGen for structural engineering is demonstrated with examples of topological shape optimization of two Extremely Modular Systems: a planar robotic manipulator Arm-Z and spatial free-form ramp Truss-Z.

Stress Constrained Topology Optimizatio,Extremely Modular System,Object-oriented software architecture,MATLAB-based array programming,First Order Reliability Analysis

This paper addresses a challenging engineering problem that combines stress-limited topology optimization, reliability analysis, and plasticity-based low-cycle fatigue. Each of these issues represents a complex problem on its own, necessitating significant computational effort. In this study, we propose a novel approach that integrates safety assessment into the topology optimization process while considering the number of cycles for low-cycle fatigue. Our method employs a linear approximation of the performance function for safety control, incorporating the number of failure cycles within a complex, multi-level load program. The methodology is validated through real experiments, using a finite element model with cubic shape functions that yield nearly identical results between numerical and experimental outcomes in the case of fatigue-resistant design for a bi-axially tensioned structural joint.

Topology optimization, stress constraints, Reliability analysis, low-cycle fatigue, fatigueplasticity

This study presents a general computational framework for topology optimization under constraints related to various engineering design problems, including: reliability analysis, low-cycle fatigue assessment, and stress limited analysis. Such a framework aims to facilitate comprehensive engineering design considerations by incorporating traditional constraints such as displacement and stress alongside probabilistic assessments of fatigue failure and the complex behaviors exhibited by structures made of elastoplastic material. The framework's amalgamation of diverse analytical components offers engineers a versatile toolkit to address intricate design challenges. Notably, the inclusion of reliability analysis introduces a probabilistic perspective, transforming conventional design constraints into random parameters, thereby enhancing the robustness of the design process.

Key to the framework's efficacy is its implementation using MATLAB mathematical computing software, leveraging the platform's efficient code execution and object-oriented programming paradigm. This choice ensures an intuitive and potent environment for designers and researchers, facilitating seamless adaptation across various engineering applications. Additionally, the proposed previously by the Authors algorithm for the topology optimization is extended by adaptive strategy allowing for efficient adjustment of an amount of material removed at individual optimization step.

The presented framework is offering a comprehensive and integrated approach to address multifaceted design challenges while enhancing design robustness and efficiency.

Topology optimization, Stress constraints, First order reliability analysis, Low-cycle fatigue, Plasticity

This paper investigates the problem of parametric identification of highly uncertain bolted connections. The unknown parameters representing stiffness of the connections are estimated using two commonly accepted methods: (1) the traditional mode matching approach and (2) a probabilistic Bayesian framework based on the maximum a posteriori (MAP) formulation. Additionally, the uncertainties of the unknown parameters are also estimated and compared for both methods. A numerical example and a real lab-scale frame structure with highly uncertain bolted connections were used in the tests. In the experimental case, the system eigenvalues (squares of the natural frequencies) and the mode shapes measured in a broad frequency range were employed. The measured mode shapes were strongly disturbed by assembly discrepancies of the bolted connections. Finally, both methods were compared in terms of computational efficiency on a large-scale FE model (31,848 degrees of freedom). Despite the sophistication of the Bayesian approach in treating the trade-off between measurement errors and expected modeling errors, the results indicate that the two tested methods yield similar values for the unknown parameters. The Bayesian approach requires numerical regularization to calculate the parameter covariance matrix, which may decrease its reliability. In contrast, the mode matching method avoids such numerical difficulties. Furthermore, the Bayesian approach requires a much larger number of iterations and a careful selection of the weighting parameters.

Mode matching, Bayesian approach, Parametric identification, Uncertain bolted connections, Parameter uncertainty, Convergence

Nowadays, consumer electronics offer computer-vision-based (CV) measurements of dynamic displacements with some trade-offs between sampling frequency, resolution and low cost of the device. This study considers a consumer-grade smartphone camera based on complementary metal-oxide semiconductor (CMOS) technology and investigates the influence of its hardware limitations on the estimation of dynamic displacements, modal parameters and stiffness parameters of bolted connections in a laboratory structure. An algorithm that maximizes the zero-normalized cross-correlation function is employed to extract the dynamic displacements. The modal parameters are identified with the stochastic subspace identification method. The stiffness parameters are identified using a model-updating technique based on modal sensitivities. The results are compared with the corresponding data obtained with accelerometers and a laser distance sensor. The CV measurement allows lower-order vibration modes to be identified with a systematic (bias) error that is nearly proportional to the vibration frequency: from 2% for the first mode (9.4 Hz) to 10% for the third mode (71.4 Hz). However, the measurement errors introduced by the smartphone camera have a significantly lower influence on the values of the identified stiffness parameters than the numbers of modes and parameters taken into account. This is due to the bias–variance trade-off. The results show that consumer-grade electronics can be used as a low-cost and easy-to-use measurement tool if lower-order modes are required.

computer vision,smartphone camera,system identification,model updating,uncertain bolted connections

Computer vision (CV) methods for measurement of structural vibration are less expensive, and their application is more straightforward than methods based on sensors that measure physical quantities at particular points of a structure. However, CV methods produce significantly more measurement errors. Thus, computer vision-based structural health monitoring (CVSHM) requires appropriate methods of damage assessment that are robust with respect to highly contaminated measurement data. In this paper a complete CVSHM framework is proposed, and three damage assessment methods are tested. The first is the augmented inverse estimate (AIE), proposed by Peng et al. in 2021. This method is designed to work with highly contaminated measurement data, but it fails with a large noise provided by CV measurement. The second method, as proposed in this paper, is based on the AIE, but it introduces a weighting matrix that enhances the conditioning of the problem. The third method, also proposed in this paper, introduces additional constraints in the optimization process; these constraints ensure that the stiff ness of structural elements can only decrease. Both proposed methods perform better than the original AIE. The latter of the two proposed methods gives the best results, and it is robust with respect to the selected coefficients, as required by the algorithm.

computer vision,structural health monitoring,physics-based graphical models,augmented inverse estimate,model updating,non-negative least square method

Structural vibrations have adverse effects and can lead to catastrophic failures. Among various methods for mitigation of vibrations, the semi-active control approaches have the advantage of not requiring a large external power supply. In this paper, we propose and test a sliding mode control method for the semi-active mitigation of vibrations in frame structures. The control forces are generated in a purely dissipative manner by means of on/off type actuators that take the form of controllable structural nodes. These nodes are essentially lockable hinges, modeled as viscous dampers, which are capable of the on/off control of the transmission of bending moments between the adjacent beams. The control aim is formulated in terms of the displacement of a selected degree of freedom. A numerically effective model of such a node is developed, and the proposed control method is verified in a numerical experiment of a four-story shear structure subjected to repeated random seismic excitations. In terms of the root-mean-square displacement, the control reduced the response by 48.4-78.4% on average, depending on the number and placement of the applied actuators. The peak mean amplitude at the first mode of natural vibrations was reduced by as much as 70.6-96.5%. Such efficiency levels confirm that the proposed control method can effectively mitigate vibrations in frame structures.

semi-active control,sliding mode control,structural control,controllable nodes,on/off nodes,damping of vibrations

The area affected by the earthquake is vast and often difficult to entirely cover, and the earthquake itself is a sudden event that causes multiple defects simultaneously, that cannot be effectively traced using traditional, manual methods. This article presents an innovative approach to the problem of detecting damage after sudden events by using interconnected set of deep machine learning models organized in a single pipeline and allowing for easy modification and swapping models seamlessly. Models in the pipeline were trained with a synthetic dataset and were adapted to be further evaluated and used with unmanned aerial vehicles (UAVs) in real-world conditions. Thanks to the methods presented in the article, it is possible to obtain high accuracy in detecting buildings defects, segmenting constructions into their components and estimating their technical condition on the basis of a single drone flight.

Seismic measurements, Safety, Training data, Earthquakes, Computer vision, Machine learning, Autonomous aerial vehicles, Drones, Synthetic data

In modern mechanical engineering, vibrations play an extremely important role. Even with small variable loads, the lack of properly conducted analysis of vibrations or dynamic stability may lead to irreversible damage. The use of modern solutions such as the implementation of piezoceramic elements, appropriately selected damping, specially designed heads in loaded slender systems or heat treatment resulting in enhancement of internal structure of the material allows one to design modern and durable structures.

vibrations, mechanical waves, heat propoagation

Although the study of oscillatory motion has a long history, going back four centuries, it is still an active subject of scientific research. In this review paper prospective research directions in the field of mechanical vibrations were pointed out. Four groups of important issues in which advanced research is conducted were discussed. The first are energy harvester devices, thanks to which we can obtain or save significant amounts of energy, and thus reduce the amount of greenhouse gases. The next discussed issue helps in the design of structures using vibrations and describes the algorithms that allow to identify and search for optimal parameters for the devices being developed. The next section describes vibration in multi-body systems and modal analysis, which are key to understanding the phenomena in vibrating machines. The last part describes the properties of granulated materials from which modern, intelligent vacuum-packed particles are made. They are used, for example, as intelligent vibration damping devices.

mechanical vibrations, energy harvesting, modal analysis, granular material

The contents of this special issue comprise four research papers devoted to engineering optimization, three of which were presented during the 2nd edition of the Workshop on Engineering Optimization (WEO-2021). The workshop was held in Warsaw, Poland, on October 7–8, 2021. Due to the COVID-19 pandemic, the 2021 edition of the workshop was organized in a hybrid form and was dedicated to the exchange of experiences in the field of engineering optimization including its theoretical and algorithmic aspects as well as practical applications. The workshop hosted six invited lectures and six thematic sessions. 21 presentations by authors from seven European and non-European countries (50% of them from outside Poland) were delivered.
Additionally, the organization of the second edition of WEO was supported by the project entitled Development of regional network on autonomous systems for structural health monitoring financed by the Visegrad Fund, under the grant agreement 22110360. More details on the workshop and the V4SHM project can be found on the following website: http://v4shm.ippt.pan.pl.

The objective of this study is to propose a relatively simple and efficient method for reliability based topology optimization for structures made of elasto-plastic material. The process of determining the optimal topology of elasto-perfectly plastic structures is associated with the removal of material from the structure. Such a process leads to weakening of structural strength and stiffness causing at the same time increase the likelihood of structural failure. An important aspect of engineering design is to track this probability during the optimization process and not allow the structure safety to exceed a certain level specified by the designer. The purpose of this work is to combine the previously developed yield-limited topology optimization method with reliability analysis using first order approach. Effectiveness of the proposed methodology is demonstrated on benchmark problems proposed by Rozvany and Maute, and the elasto-plastic topology design of L-shape structure which is frequently used in different approaches for stress constrained topology optimization.

topology optimization, reliability analysis, elasto-plastic analysis

In this study, a novel modal control strategy by means of semi-actively lockable joints is proposed. The control strategy allows for a directed flow of energy between vibrational modes, which makes it suitable not only for vibration attenuation purposes but also for energy scavenging driven by electromechanical energy harvesters. The proposed control strategy is an extension of the prestress-accumulation release (PAR) technique; however, it introduces also new concepts that increase the efficiency of the overall control system. Contrary to the PAR, the proposed method requires measurement of both strains in the vicinity of the semi-active joints and translational velocities that provide global information about system behavior. The latter aspect requires the control system to be organized within a hierarchical feedback architecture. The benefit from this higher complexity of the control system is its better performance compared to the PAR. The proposed semi-active modal control not only attenuates structural vibration faster, but it also achieves this goal with a smaller number of switches implemented in the joints. The effectiveness of the proposed methodology has been demonstrated on structures equipped with two lockable joints. Two practical examples have been investigated: one employs the concept of vibration-based energy harvesting for a two-story frame structure, while the second one reduces vibration of an eight-story frame structure subjected to kinematic excitation.

energy harvesting, lockable joint, modal coupling, semi-active control, vibration attenuation

This paper proposes a computationally effective framework for load‐dependent optimal sensor placement in large‐scale civil engineering structures subjected to moving loads. Two common problems are addressed: selection of modes to be monitored and computational effectiveness. Typical sensor placement methods assume that the set of modes to be monitored is known. In practice, determination of such modes of interest is not straightforward. A practical approach is proposed that facilitates the selection of modes in a quasi‐automatic way based on the structural response at the candidate sensor locations to typical operational loads. The criterion used to assess sensor placement is based on Kammer's Effective Independence (EFI). However, in contrast to typical implementations of EFI, which treat the problem as a computationally demanding discrete problem and use greedy optimization, an approach based on convex relaxation is proposed. A notion of sensor density is applied, which converts the original combinatorial problem into a computationally tractable continuous optimization problem. The proposed framework is tested in application to a real tied‐arch railway bridge located in central Poland.

optimal sensor placement, effective independence method, Fisher information matrix

This work is an effort to join, for the first-time, multifractal analysis and damage detection in civil structures subjected to strong ground seismic motions. Specifically, based on the singularity spectrum quantitative and qualitative criteria are proposed. The qualitative criteria are based on the concave of singularity spectrum of damage and undamaged structure. The proposed quantitative criterion is based on calculation of damage index taken the parameters of singularity spectrum. In order to achieve the above goal, a robust signal processing method, which is known as multifractal wavelet leader (MFWL) is used. The multifractal analysis is a tool to calculate fractal properties as well as scaling behavior of the structural response excited by an earthquake. The singularity spectrum is obtained from the Legendre-transformation to Holder exponents. In this paper, a parameter which is based on the shape of singularity spectrum and can identify the damage in the structure is proposed. The proposed method is an output-only approach for damage detection. Considering that the dynamic behavior of an inelastic system subjected to strong ground motion appears to be a non-stationary process, the above procedure of multifractal wavelet leader is suitable to retrieve the simulation response data. The findings from the analysis show that the MFWL is an appropriate scheme for structural damage detection.

multifractal wavelet leader, damage detection, singularity spectrum, earthquake engineering, structural safety

This study is devoted to a novel method for topology optimization of elastoplastic structures subjected to stress constraints. It should be noted that in spite of the classical solutions of the different type of elastoplastic topology problems are more than 70 years old, the integration of the Prandtl-Reuss constitutive equations into the topology optimization process is not very often investigated in the last three decades. In the presented methodology where the classical variational principles of plasticity and the functor-oriented programming technique are applied in topology design, the aim is to find a minimum weight structure which is able to carry a given load, fulfills the allowable stress limit, and is made of a linearly elastic, perfectly plastic material. The optimal structure is found in an iterative way using only a stress intensity distribution and a return mapping algorithm. The method determines representative stresses at every Gaussian point, averages them inside every finite element using the von Mises yield criterion, and removes material proportionally to the stress intensities in individual finite elements. The procedure is repeated until the limit load capacity is exceeded under a given loading. The effectiveness of the methodology is illustrated with three numerical examples. Additionally, different topologies are presented for a purely elastic and an elastoplastic material, respectively. It is also demonstrated that the proposed method is able to find the optimal elastoplastic topology for a problem with a computational mesh of the order of tens of thousands of finite elements.

topology optimization,elastoplastic structures,minimum-weight design,stress constraints

The main drawback of vibration-based energy harvesting is its poor efficiency due to small amplitudes of vibration and low sensitivity at frequencies far from resonant frequency. The performance of electromagnetic energy harvester can be improved by using mechanical enhancements such as mechanical amplifiers or spring bumpers. The mechanical amplifiers increase range of movement and velocity, improving also significantly harvester efficiency for the same level of excitation. As a result of this amplitude of motion is much larger comparing to the size of the electromagnetic coil. This in turn imposes the need for modelling of electromagnetic circuit parameters as the function of the moving magnet displacement. Moreover, high velocities achieved by the moving magnet reveal nonlinear dynamics in the electromagnetic circuit of the energy harvester. Another source of nonlinearity is the collision effect between magnet and spring bumpers. It has been shown that this effect should be carefully considered during design process of the energy harvesting device. The present paper investigates the influence of the above-mentioned nonlinearities on power level generated by the energy harvester. A rigorous model of the electromagnetic circuit, derived with aid of the Hamilton's principle of the least action, has been proposed. It includes inductance of the electromagnetic coil as the function of the moving magnet position. Additionally, nonlinear behaviour of the overall electromagnetic device has been tested numerically for the case of energy harvester attached to the quarter car model moving on random road profiles. Such a source of excitation provides wide band of excitation frequencies, which occur in variety of real-life applications.

energy harvesting, velocity amplification, nonlinear electromagnetic circuit, spring bumper, quarter car model

This paper describes a semi-active control strategy that allows to transfer the vibration energy from an arbitrarily induced to a selected structural mode. The intended aim of the proposed control strategy is energy harvesting from structural vibrations. Another potential application is related to structural safety. In the paper, a mathematical model is first introduced to describe the phenomenon of vibrational energy transfer, and then, based on this model, an efficient semi-active control strategy is proposed. Finally, some problems related to measurement techniques are discussed. The effectiveness of the proposed methodology is demonstrated in an example of energy transfer between vibrational modes of a three-bar planar frame structure.

vibration energy, modal control, lockable joint, modal coupling

The paper deals with a novel approach to development of optimality criteria based finite element code for topology optimization of elasto-plastic structures. The novelty of this work is related to the concept of function object called functor and its application to efficient FE code development. First, the general problem of topology optimization under stress constraints is briefly formulated. Then, the programming aspects of topology optimization using traditional object-oriented and functor based programming are discussed. The advantages of the functor based approach are related to simplicity of designing the FE code architecture and reusability of this code. In particular the metric known as 'Lack of cohesion of methods' is useful in comparing these two different paradigms. Finally, the paper is also illustrated with numerical examples of topology optimization using the proposed methodology.

topology optimization, function object, functor programming, optimal design, elasto-plastic structures, finite element programming

Damage identification forms a key objective in structural health monitoring. Several state-of-the-art review papers regarding progress in this field up to 2011 have been published. This paper summarizes the recent progress between 2011 and 2017 in the area of damage identification methods for bridge structures. This paper is organized based on the classification of bridge infrastructure in terms of fundamental structural systems, namely, beam bridges, truss bridges, arch bridges, cable-stayed bridges, and suspension bridges. The overview includes theoretical developments, enhanced simulation attempts, laboratory-scale implementations, full-scale validation, and the summary for each type of bridges. Based on the offered review, some challenges, suggestions, and future trends in damage identification are proposed. The work can be served as a basis for both academics and practitioners, who seek to implement damage identification methods in next-generation structural health monitoring systems.

arch bridge, beam bridge, cable‐stayed bridge, damage identification, suspension bridge, truss bridge

The present study deals with a comprehensive approach for damage identification of spatial truss structures. The novelty of the proposed approach consists of a three-level analysis. First, sensitivity of assumed modal characteristics is calculated. Second, natural frequency sensitivity is used to determine hardly identifiable structural parameters and mode shape sensitivity is applied to select damage-sensitive locations of sensors. Third, two sparsity constrained optimization algorithms are tested towards efficient identification of applied damage scenarios. These two algorithms are based on ℓ1-norm minimization and non-negative least square (NNLS) solution. Performances of both proposed algorithms have been compared in two realistic case studies: the first one concerned a three-dimensional truss girder with 61 structural parameters and the second one was devoted to an upper-deck arch bridge composed of 416 steel members.

sensor placement, damage identification, ℓ1-norm minimization, sparsity constrained optimization

This study proposes a neural network based vibration control system designed to attenuate structural vibrations induced by an earthquake. Classical feedback control algorithms are susceptible to parameter changes. For structures with uncertain parameters they can even cause instability problems. The proposed neural network based control system can identify the structural properties of the system and avoids the above mentioned problems. In the present study it is assumed that a full state of the structure is known, which means the at each floor horizontal displacements and rotations about the vertical axis are measured. Additionally, it is assumed the acceleration signal coming from the earthquake is also available. The proposed neural control strategy is compared with the classical linear quadratic regulator (LQR) not only in terms of displacement responses, but also required control forces. Moreover, the influence of different weighting matrices on performance of the proposed control strategy has been presented.
The effectiveness of the neuro-controller has been demonstrated on two numerical examples: a simple single degree of freedom (DOF) structure and a multi-DOF structure representing a twelve story building. Both structures under consideration have been excited with El Centro acceleration signal. The results of numerical simulations on the SDOF system indicate that using neuro-controller it would be possible to obtain smaller amplitudes as compared with the LQ regulator, but it would require higher control effort.

vibration control, artificial neural networks, seismic excitation

This work proposes an efficient and reliable method for damage localization in truss structures. The damage is localized on the basis of measured acceleration signals of the structure followed by simple statistical signal processing. It has three main advantages over many existing methods. Firstly, it can be directly applied to real engineering structures without the need of identifying modal parameters or solving any global optimization problem. Secondly, the proposed method has higher sensitivity to damage than some other frequently used methods and allows to localize damage as small as a few percents. Thirdly, it is a model-free method, which does not require precise finite element model development or updating. Validation of the method has been conducted on numerical examples and laboratory-scale trusses. Two types of frequently used trusses have been selected for this study, namely Howe and Bailey trusses. The presented experimental validation of the method shows its efficiency and robustness for damage localization in truss structures.

structural health monitoring, truss structures, damage detection

The purpose of this work is the development of an efficient and high-sensitive damage localization technique for truss structures, based on the rank-revealing QR decomposition (RRQR) of the difference-of-flexibility matrix. The method is an enhancement of the existing techniques of damage detection, which rely on the set of so-called damage locating vector (DLV). The advantages of the RRQR decomposition-based DLV (RRQR-DLV) method are its less computational effort and high sensitivity to damage. Compared with the frequently used stochastic DLV (SDLV) method, RRQR-DLV offers higher sensitivity to damage, which has been validated based on the presented numerical simulation. The effectiveness of the proposed RRQR-DLV method is also illustrated with the experimental validation based on a laboratory-scale Bailey truss bridge model. The proposed method works under ambient excitation such as traffic excitation and wind excitation; therefore, it is promising for real-time damage monitoring of truss structures.

damage localization, rank-revealing QR decomposition, damage sensitivity, truss structure, structural health monitoring

The purpose of this study is to present an optimal design procedure for elasto-plastic structures subjected to impact loading. The proposed method is based on mode approximation of the displacement field and assumption of constant acceleration of impacted structure during whole time of deformation process until the plastic displacement limit is reached. Derivation of the method begins with the application of the principle of conservation of linear momentum, followed by determination of inertial forces. The final stage of the method utilizes an optimization technique in order to find a minimum weight structure. Eventually, effectiveness and usefulness of the proposed method is demonstrated on the example of a planar truss structure subjected to dynamic loading caused by a mass impacting the structure with a given initial velocity.

structural dynamics, optimal design, elasto-plastic structures, short-time dynamic loading

The paper deals with non-linear analysis of a telecommunication tower with circular flange-bolted connections (CFBCs). They are composed of two flanges, welded to the structural tubes, and then connected together with pre-tensioned bolts. A rigorous FEM analysis is performed for finding the connection stiffness in two cases. One deals with all bolts undamaged and the second one with one or more bolts broken.

The analysis, which includes contact and friction forces, shows that when joints are under tension, the bolts are not only subjected to axial forces, but also to bending moments due the prying effect. The value of stresses caused by bending depends strongly on the bolt pre-tension and flange thickness. Removing one of the six connection bolts significantly increases stresses in the remaining bolts. Knowing the behaviour of the connection, it is possible to study the behaviour of the whole structure. This is achieved by applying the multilevel substructuring approach. The first levels is related to the flanges and bolts, whereby the connection model is simplified, and compared with the rigorous one, the second level is related to the assembly of the whole tower.

The paper is illustrated with several examples of connections of different thicknesses, and different bolt pre-tensions. The considered tower comes from a real design.

Bolted flange connection, Contact forces, Friction forces, Non-linear FEM analysis, Substructuring, Telecommunication tower, Structural connection damage, Structural health monitoring

We present an efficient and robust damage localization method. Its applications therefore include defect location in shear buildings and beam structures. The proposed method is based on the knowledge of the difference of curvatures, computed for a structure before and after damage occurs. However, instead of using modal shapes for this purpose, as is frequently performed, the present method computes the curvature directly from acceleration signals, without identifying modal shapes of the structure. Additionally, the accelerations are subjected to averaging, which reduces measurement noise, and logarithm extraction, which renders the method independent of the amplitude of the loading impulse used for damage location. Another important feature of the method is that it does not require any calibration of numerical models, because it is solely based on measurement data. The presented method of damage location is illustrated with two examples, which involve experimental tests on laboratory-scale structures. The first example concerns defect location in a shear-building structure, and the second one in a spatially excited simply supported steel beam. Both cases confirm the effectiveness of the method, and its robustness to measurement noise.

degree of dispersion, transient response-based damage detection, robust damage localization, shear buildings, beam structures

This paper describes an application of wavelet analysis for damage detection of a steel frame structure with bolted connections. The wavelet coefficients of the acceleration response for the healthy and loosened connection structure were calculated at each measurement point. The difference of the wavelet coefficients of the response of the healthy and loosened connection structure is selected as an indicator of the damage. At each node of structure the norm of the difference of the wavelet coefficients matrix is then calculated. The point for which the norm has the higher value is a candidate for location of the damage. The above procedure was experimentally verified on a laboratory-scale 2-meter-long steel frame. The structure consists of 11 steel beams forming a four-bay frame, which is subjected to impact loads using a modal hammer. The accelerations are measured at 20 different locations on the frame, including joints and beam elements. Two states of the structure are considered: healthy and damaged one. The damage is introduced by means of loosening two out of three bolts at one of the frame connections. Calculating the norm of the difference of the wavelet coefficients matrix at each node the higher value was found to be at the same location where the bolts were loosened. The presented experiment showed the effectiveness of the wavelet approach to damage detection of frame structures assembled using bolted connections.

complex bolted lap connection, frame structure, wavelet analysis, damage detection

An experimental and analytical study of the relation between local defect, in a steel structure, and its higher frequencies and higher modes is discussed. The structure is a plane steel frame, assembled of beams, joined together with bolted connections. Removing some bolts from a given connection simulates the damage. In the experiment, an impulse force induced structural vibrations. Effects of vibrations were shown by data from gages, measuring accelerations with a high accuracy. From the data, it could be observed, that mode shapes, for the healthy and damaged structures didn’t show any differences for low frequencies. Only modes around thirteen showed significant gap between picks of Frequency Response Functions, for healthy and damaged frame. Moreover, looking at mode shapes, it could be observed that structural configuration may have some influence on defects to be observable. This aspect is discussed in a separate section. The experiment performed on the whole structure allows finding the place where the defect is localized. However, it can’t give detailed information on the defect itself, here defect of a bolt. For finding it, an ultrasonic measurement of pre-tensioning forces in bolts was applied. It allowed not only to determine stresses in the bolt, but also to verify, if in the process of assembling the structure was not pre-stressed.

Detectable damages, Bolted connections, Experimental modal analysis, Ultrasonic measurements, Steel frames, Analytical dynamics

In this study, a relatively simple method of discrete structural optimization with dynamic loads is presented. It is based on a tree graph, representing discrete values of the structural weight. In practical design, the number of such values may be very large. This is because they are equal to the combination numbers, arising from numbers of structural members and prefabricated elements. The starting point of the method is the weight obtained from continuous optimization, which is assumed to be the lower bound of all possible discrete weights. Applying the graph, it is possible to find a set of weights close to the continuous solution. The smallest of these values, fulfilling constraints, is assumed to be the discrete minimum weight solution. Constraints can be imposed on stresses, displacements and accelerations. The short outline of the method is presented in Sec. 2. The idea of discrete structural optimization by means of graphs. The knowledge needed to apply the method is limited to the FEM and graph representation.

discrete structural optimization, combinatorial optimization, structural dynamics, stochastic loading, problem oriented optimization, graphs

The paper is concerned with a minimum weight design of composite floors subjected to dynamic loading, deriving from the rhythmic activity of a group of people. The floor structure consists of concrete slab cast, on thick trapezoidal deck, which is supported by a grid of steel beams. The structure is vibration-prone and exhibits a number of natural frequencies, which are within a range of loading function. Minimum weight design consists in assigning, from catalogues of prefabricated plates and beams appropriate elements assuring fulfillment of imposed constraints on displacements and accelerations. Applied, practical discrete optimization method is based on graph theory and finite element analysis. Efficiency of the proposed design is demonstrated in an example of real-world engineering structure.

structural optimization, discrete optimization, structural vibrations, omposite floor structure

Many optimum structural designs are based on searching for the best of all combinations, arising from the number of structural members, and parameters of listed rolled profiles. Even, in a relatively simple design, the number of such combinations is of an order higher than ten. All known methods of finding discrete minimum of structural weight require very large number of analyses often of an order of four. In this study, are relatively simple method of solving such problems is presented. It is based on a tree graph, representing discrete values of the structural volume. The structure can be subjected to multi static loadings with constraints imposed on displacements and stresses. The number of analyses, in the proposed algorithm, is limited to the order of two. The knowledge needed to apply the method is limited to FEM and graph representation. The paper is illustrated with two examples with numbers of combinations up to 42 to the power 38.

Structural optimization, Problem oriented optimization, Discrete optimization, Combinatorial optimization, Graphs

A very simple method for finding the minimum weight of a structure designed from a list of available parameters is presented. The structure can be subjected to multiple loading conditions with constraints imposed on displacements, stresses and eigenfrequency. The method consists of a recursive removal of redundant material, starting from the heaviest structure. The number of analyses required is a factor of 10 to the power 2 less than for most stochastic methods. The knowledge needed for application of the method is limited to the finite-element method.

structural optimization, combinatorial optimization, structural dynamics

A very simple discrete optimization algorithm for minimum structural weight is presented. The main idea consists in assigning initial cross-sections to a given structure, and then searching for its least stressed elements. In the second stage of the algorithm, the cross-section of the element with minimum stress is reduced to the next catalogue entry. Such reduction of cross-sections is continued until imposed bounds are met. The presented algorithm was positively tested on example configurations with complexity of 10 to the power 10 and 30 to the power 8 combinations.

discrete optimization, truss structures

The purpose of this work is to present an algorithm for optimal vibration control of guyed masts and an example of its application to a numerical simulation. The objective of the proposed control system is to minimize amplitudes of transverse vibrations of the top of a mast induced by wind pressure acting on the structure. Control forces are assumed to be physically realized through changes of tension in guy cables, supporting the mast. The only required measurements are velocities of guy cables at the anchor-points. On the basis of those, a complete state of deformation of the structure is obtained by using the Kalman filter. The Davenport spectral density function is adopted as a model of the stochastic action of the wind.

structural vibrations, vibration control, guyed masts, wind fluctuations

In the paper two methods of real-time load identification are proposed. The first one is based on information about frequency characteristics of loading, while the second one uses only information about deformation of structure. Theoretical considerations are illustrated by numerical calculations on a example of simply supported beam.

load identification, limited number of sensors

This contribution considers the problem of topology optimization of modular structures. A bionic trunk-like robotic “Arm-Z” manipulator is considered. The manipulator is modular, that is, it is composed of a sequence of identical modules. In geometric terms, each module is essentially an obliquely cut section of an elliptical pipe, so in the cutting plane it forms a circle. With respect to the previous module, it has a single degree of freedom: the relative twist. Therefore, the total number of the degrees of freedom of the entire manipulator equals the number of its modules. Such a manipulator belongs to the family of Extremely Modular Systems. The advantages of such systems are the economization (due to the possible mass production of modules) and robustness (replacement of a failed module instead of a complex repair).

Topology optimization, Modular manipulator, Multiple loadings, Geometric transformations, Kinematics, Stress constraints.

This contribution applies the machine learning technique of reinforcement learning for simultaneous damage detection and control of structures. The proposed system consists of two components. The control component is responsible for semi-active mitigation of vibrations. The control law is determined experimentally in a trial-and-error interaction with a simulated environment. The process is data-driven: the control agent iteratively improves its control law based on the observed results of past control actions. The robustness relies on the accuracy of the structural model used for training. The control efficiency can decrease if the physical structure is damaged and diverges from the model, that is, when effective control may be most required. Thus, the second component of the proposed system monitors the structure to detect damages and inform the control component. The approach is tested in a numerical experiment of a shear-building under random seismic-type excitation. A semi-active tuned mass damper (TMD) is used as an actuator, and a classical TMD serves as a reference.

semi-active control, structural control, structural monitoring, reinforcement learning, machine learning

Classical approaches to attenuation of vibrations usually aim at dissipation or absorption of the vibration energy in especially designed devices mounted to the structure. A less common approach but recognised as very effective is to induce mechanisms of transferring the vibration energy associated with low-frequency modes into higher-order vibration modes, where it is quickly dissipated by material damping (in structural volume). In the present work, a novel semi-active modal control methodology is proposed for precise control of mechanical energy transfer between vibration modes by means of lockable joints. Moreover, this control strategy is well-suited also for energy harvesting purposes. Energy of the currently induced vibration modes can be transferred into a preselected structural vibration mode that is tuned with an energy harvester. The proposed control strategy is verified numerically, whereas its experimental validation is shown in the accompanying article within the present proceedings.

In this work an experimental study is presented aiming at demonstration of a controlled modal energy transfer concept in frame structures equipped with semi-active members. The proposed semi-active members – lockable joints – allow for local modification of the frame’s stiffness. The objective of the introduced control approach is to provide mechanical energy transfer between particular eigenmodes. A demonstrator has been fabricated for the purpose of the investigation consisting of a double beam frame structure in a cantilever configuration, which is equipped with the semi-active members. The investigated control algorithm employs two types of input signals: local velocity of the structure and local strain of the frame. As a result, a verification of the system effectiveness has been revealed in a variety of frequency ranges. The excitation bandwidth has been appropriately suited to the particular tested cases. The experimentally obtained results confirmed a possibility of the energy transfers between particular structural eigenmodes.

This contribution presents a semi-active control technique intended for mitigation of structural vibrations. The control law is derived in a repeated trial-and-error interaction between the control agent and a simulated environment. The experience-based training approach is used which is the defining feature of the machine learning techniques of reinforcement learning (RL), implemented here using the framework provided by Deep Q Learning (DQN). The involved artificial neural network not only determines the control action, but additionally identifies structural damages, which is a nontrivial task due to the nonlinearity of the control. This requires a specific multi-head architecture, which allows the network to be damage-aware, and a specific training procedure, where the memory pool preserved for the RL stage of experience replay is populated with not only the observations, control actions, and rewards, but also with the momentary status of structural damage. Such an approach can be used to explicitly promote the damage-awareness of the control agent. The proposed technique is tested and verified in a numerical example of a shear-type building model subjected to a random seismic-type excitation. A tuned mass damper (TMD) with a controllable level of viscous damping is used to implement the semi-active actuation, and the optimally tuned classical TMD provides the reference response.

semi-active control, tuned mass damper (TMD), reinforcement learning, damage identification

This paper considers structural control by reinforcement learning. The aim is to mitigate vibrations of a shear building subjected to an earthquake-like excitation and fitted with a semi-active tuned mass damper (TMD). The control force is coupled with the structural response, making the problem intrinsically nonlinear and challenging to solve using classical methods. Structural control by reinforcement learning has not been extensively explored yet. Here, Deep-Q-Learning is used, which appriximates the Q-function with a neural network and optimizes initially random control sequences through interaction with the controlled system. For safety reasons, training must be performed using an inevitably inexact numerical model instead of the real structure. It is thus crucial to assess the robustness of the control with respect to measurement noise and model errors. It is verified to significantly outperform an optimally tuned conventional TMD, and the key outcome is the high robustness to measurement noise and model error.

structural control, semi-active control, reinforcement learning, tuned mass damper (TMD)

Vibration control is a crucial issue in engineering, necessitating the continuous development and refinement of effective control strategies. In the present study, a semi-active control methodology utilizing lockable joints is investigated. The lockable joints provide a modal coupling effect, resulting in controlled energy transfer between vibration modes. Numerical simulations demonstrate that energy can be transferred to higher-order vibration modes and rapidly dissipated through inherent material damping or transferred to a preselected vibration mode for energy harvesting.

Semi-active modal control, Smart Structures, Lockable joints, Energy transfer, Vibration damping

In this study an experimental program for verification of modal control algorithm for semi-active structures is proposed. The considered control approach assumes redirecting of mechanical energy between vibrational modes. The presented research is focused on development of an investigation method that would allow for demonstrating the control concept. Moreover, a suitable flexible structure equipped with semi-active elements is introduced. The proposed laboratory structure is a flat slender frame equipped with a set of six joints. A deliberate design of the joints provides a feasibility for a controllable transfer of the bending moments between chosen adjacent elements of the frame. Such a structure delivers a possibility of real-time modification of its local bending stiffness and therefore can be categorised as semi-active. The investigation covers identification of the modal parameters of the laboratory model, implementation of the control algorithm on an FPGA processor, providing a testing program that exemplifies the process of energy management between the eigenfrequencies. The results reveal that the response of the semi-active structure reflects the derived control algorithm assumptions. To sum up, the modal control algorithm based on real-time monitoring of the structure's modal parameters is experimentally implemented and verified in a laboratory environment.

vibration control, semi-active, modal control, experimental verification, lockable joints

The methodology for optimal single-type sensor placement has been extensively discussed in the literature. However, little attention has been devoted to the distribution of multi-type sensors. The application to large structures, such as bridges or towers, poses a significant challenge. Some responses, for example, the displacements of a bridge over a river, cannot be easily measured directly. Consequently, indirect techniques can be employed to estimate the deflections of such structures. In this contribution, a Kalman filter-based algorithm is presented to address this sensor placement problem. The effectiveness of the proposed method is numerically demonstrated using the example of an actual tied-arch bridge.

sensors, optimal sensor placement, Kalman filter, reduced order model, arch bridge

This contribution presents a sliding-mode control approach for the mitigation of vibrations in frame-like structures. The control is implemented in a semi-active manner, that is, without significant external control forces and substantial power consumption, which are typical for active control approaches. Here, the control is achieved through dynamic, lowcost modification of properties at selected structural nodes. The employed actuators have the untypical form of two-state hinges, which can switch between two extreme states: no transfer of bending moments (effectively a hinge) and full transfer of bending moments (a locked hinge or a typical frame node). Consequently, the control forces are dissipative and coupled to the response. Previous research in this area focused on purely energetic considerations, aiming for global damping of vibrations. In contrast, this paper formulates the control objective in terms of local displacements of a selected degree of freedom, which can be interpreted as the task of isolating it from external excitations. This formulation is employed to define the target sliding hyperplane. The state of the actuators is chosen such that the effective control forces push the structural state toward the target hyperplane. The approach is verified in a numerical example of a six-story shear-type structure subjected to random seismic excitation.

Structural control, Semi-active control, Sliding mode control, On/off nodes

This contribution presents an approach to structural control based on reinforcement learning. Reinforcement learning, a rapidly developing branch of machine learning, is based on the paradigm of learning through interaction with the environment. Here, it is applied in the context of semi-active structural control, where the considered actuators take the form of viscous dampers with a controllable level of damping. The control forces are thus coupled with the structural response, and the formulation is intrinsically nonlinear. The related optimum control problems are usually more difficult than in the case of active structural control systems, which generate and apply arbitrary external control forces. Analytical derivation of the optimum semi-active control is thus rarely possible, so that many control algorithms applied in practice are suboptimal and/or heuristic in nature. Here, an effective control strategy is developed by means of the Q-learning approach. The control algorithm is determined in interaction with the controlled system, that is, by applying initially random control sequences in order to observe, process, and optimize their effects. Such an approach seems to be new and relatively unexplored in the field of structural control. Verification is performed in a numerical experiment, where the Q-learning procedures interact with an independently simulated finite element model of a structure equipped with a tuned mass damper (TMD) and a controllable viscous damper. The results attest to a performance significantly better than that of an optimally tuned conventional TMD.

Reinforcement Learning, Semi-active control, Structural control, Damping, Vibration

In the present study a comparison of frequently used computer vision (CV)-based methods for structural health monitoring of truss structures is shown. The attention is paid to template matching methods that can be classified into one of two groups: area-based and feature-based methods. Synthetic but realistic video is used in this study. Results of the comparison are reliable due to the fact that the exact displacements are known from the finite element model of the investigated structure. From the variety of tested CV methods, the Kanade–Lucas–Tomasi algorithm with FREAK-based repetitive correction outperforms the remaining tested methods in terms of the computation time with a negligibly greater estimation error.

computer vision, structural health monitoring, physics-based graphics models (PBGM), IC-SHM 2021, benchmark test

In this study we show pros and cons of two frequently used approaches for model updating and parametric identification of structural system assembled by uncertain bolted connections. The comparison between classical mode matching and a recently proposed Bayesian approach is demonstrated. Classical methods for modal updating based on modal sensitivity require matching of modal parameters extracted from measurement data with those obtained numerically. Alternative approach is based on a probabilistic framework with the aid of Bayesian methodology. Such an approach explicitly includes the problem of a trade-off between modeling and measurement errors. These two methods are compared an a laboratory-scale three-story frame with unknown parameters corresponding to bolted connections. A total of 82 degrees of freedom are measured using 4 bidirectional accelerometers and roving sensor technique.

Performance of any Structural Health Monitoring (SHM) system strongly depends on a set of sensors which are distributed over the structure under investigation. Optimal deployment of sensors on large scale structures such as tied-arch bridges is quite a challenging problem. Moreover, deployment of a sensor network consisting of different types of sensors (accelerometers, inclinometers or strain gauges) over a large scale bridge renders the task of optimization even more demanding. In the present study, a conventional sensor placement method for distribution of a homogenous sensor network is expanded to the heterogeneous case. First, the basic equations governing the estimation error will be recalled. Then, the Fisher information matrix is assembled using normalized translational and rotational mode shapes. Finally, a computational procedure is proposed which allows optimal sensor positions to be selected among thousands candidate locations. The effectiveness of the proposed strategy is demonstrated using a realistic example of a tied-arch bridge located in Poland.

optimal sensor placement, structural health monitoring, tied-arch bridges, multi-type sensor network

The success of virtually all structural health monitoring (SHM) methods depends on the information content of the measurements, and thus on the placement of the available sensors. This paper presents an efficient method for finding optimal sensor distribution over structural system with many degrees of freedom (DOFs). The objective function is based on the classical Fisher information matrix. Originally, this yields a computationally hard discrete optimization problem. However, the proposed numerical solution method is based on a concept taken from structural topology optimization, where a discrete optimization problem is replaced with a continuous one. Two numerical examples demonstrate the effectiveness of the proposed methodology. These are a 5-bay truss with 24 DOFs and a two-story frame structure whose finite element model has been condensed to 14 DOFs.

This paper deals with the application of wavelet analysis on damage detection in mixed concrete/steel frame structures subjected to earthquake excitation. Such buildings are typically the result of a building initially constructed as a reinforced concrete building and, at a later time, more storeys were added as steel moment resisting frames. These structures consist of rein-forced concrete frames at the lower storeys and steel frames at the upper storeys. They are characterized by the material inconsistency in height. The proposed method of wavelet analysis of structural response is an output-only damage detection method. Non-linear dynamic analysis has been performed and response data at each story are obtained which are used as simulation data. Damage in the frame is due to hysteretic behaviour of columns and beams. Since the dynamic behaviour of an inelastic structure subjected to an earthquake excitation is a non-stationary process, discrete and continuous wavelet analysis were performed in order to re-trieve the simulation response data. The proposed method is based on the assumption that there is a correlation between structural damage, due to non-linear behaviour of structural elements and spikes that can be clearly detected in the wavelet details. This is supported by the fact that at the time when the spikes are recorded, structural damage occurs as well. The numerical results indicate that the discrete wavelet analysis is a promising method for the detection of damage in structures without the need for visual inspection.

Mixed concrete/steel frame, Damage detection, Discrete wavelet analysis, Continues wavelet analysis, Structural dynamics, Earthquake engineering

Damage identification attracted a lot of attention during the last three decades. The reason for that is the fact that large number of existing civil infrastructures reached their service life and growing number of structures is equipped with Structural Health Monitoring (SHM) systems. A successful structural damage identification is determined by three inseparably coupled factors: sensor placement, damage location and its extend, and finally location and time-frequency characteristics of the applied excitation. The purpose of this study is to address the first of the mentioned aspects, namely optimal sensor placement. A vast literature has been devoted to optimal sensor placement methods among which Effective Independence (EI) method proposed by Kammer and Tinker is one of the most successfully applied in practice. However, EI method is dedicated rather to test-analysis correlation and therefore more specific methods for damage identification are still needed. Additionally, in the case of large civil structures, which are intended to be equipped with large amount of sensors of different type, other sensor placement methods can be more efficient. Recently, a promising idea of utilizing a topology optimization approach for the purpose of sensor placement has been proposed by Bruggi and Mariani. The goal of this study is to extend their method, which has been verified on a plate structure, to the case of a FE model of a real arch bridge structure consisting a few thousands degrees of freedom. The main purpose of this work is to find the optimal arrangement of sensors on the structure to detect defects most accurately. The objective function for the problem formulated in this way is the total, weighted difference between the deformation of a damaged and undamaged state. This problem is very similar to the topological optimization, where we search for the optimal material distribution minimizing the mass of the structure while meeting the conditions related to some mechanical properties such as the maximum displacement of the structure, stress intensity or load capacity. This similarity led us to apply topological optimization to the problem of optimal placement of damage sensors. Several numerical examples prove the applicability of topological optimization for optimal sensor placement problem.

Sensor Placement, Damage Identification, Topology Optimization

Recent progress in sensing technology and measurement techniques allows a growing number of critical infrastructures to be equipped with Structural Health Monitoring (SHM) systems. Sensors in such SHM systems should be placed in a proper way to facilitate extracting valuable information from the structure under investigation. In the case of relatively simple spatial truss structures, sensors can be located with the aid of classical methods such as Effective Independence (EI) method proposed by Kammer. However, in the case of large structures, which are intended to be equipped with hundreds if not thousands of sensors, other sensor placement methods may be needed.
The goal of this study is to extend a topology optimization based approach for sensor placement (proposed originally by Mariani and co-workers) to the case of real bridge structures represented by finite element models with a few thousand degrees of freedom. Structural topology optimization aims to find the optimum material distribution in order to minimize the mass of the structure while maintaining mechanical properties (load capacity, displacements, etc.). A similar concept can be used to determine the optimal placement of sensors in a structure to identify its dynamic characteristics. The sensor positions are determined in such a way that estimation error of modal coordinates is minimized. The effectiveness of the proposed methodology is demonstrated on an example of a detailed FE model of a tied-arch bridge.

Optimal sensor placement, Structural parameter identification, Topology optimization

This contribution proposes a semi-active control approach for a directed energy transfer between structural vibrational modes. The motivation is the intended localization of the vibration energy in a selected mode for the purpose of energy harvesting and mitigation of structural vibrations. The proposed control strategy aims at the instantaneous maximization of the energy transfer to the target mode. It is based on an untypical approach of dynamic structural reconfiguration and implemented using a semi-actively controllable node: a lockable joint. Such a joint, depending on the control signal, can act as a hinge or as a typical frame node. Effectively, it provides thus an on/off ability to control the transfer of bending moments between the adjacent structural elements. The effectiveness of the approach is demonstrated in a numerical example of a plane frame structure.

Modal control, Semi-active control, Lockable joints, Energy harvesting

This paper present elasto-plastic topology optimization with reliability constraint. It recalls fundamental concepts from first order reliability analysis and introduces an algorithm for topology optimization of elasto-plastic structures. The presented numerical example shows dependence of the volume fraction on probability of failure.

Structural topology optimization, Elastoplastic analysis, Reliability based optimization

The paper presents a novel method for sensor placement optimized towards effective identification of structural damages. The derivation of the method is based on the concept of virtual distortions together with information provided by a set of strain gauges. Then, a gradient oriented optimization is applied to identify sensor locations, which are the most sensitive to potential damage scenarios. Steepest descent method is utilized to determine the optimal values of the objective function. Additionally, dependence of the method on the applied excitation signal is discussed. Finally, effectiveness of the proposed methodology is demonstrated on an example of optimal search for sensor placement on a 6-bay planar truss structure.

optimal sensor placement, virtual distortion method, damage identification

Optimal topologies obtained for structures subjected to deterministic loading can be sensitive to loading variations in terms of both magnitude and direction. Therefore, in this study we consider problem of topology optimization for structures subjected to probabilistic loading. The proposed method applies basic findings from probability theory, which allow to transform the original problem of topology optimization under single probabilistic loading into analogous problem of topology optimization under multiple deterministic loading cases. After recalling the theoretical background of the method,' its effectiveness is demonstrated on an examples of cantilever structure subjected to horizontally oriented load with randomly varying angle of action.

Topology optimization, Stochastic load, Elastoplastic FE analysis

The purpose of this study is a practical engineering formulation of the topology optimization problem for three dimensional elastoplastic structures. The present study constitutes a comprehensive approach to topology optimization of elastoplastic structures, including both the mechanical problem statement and its efficient computer implementation. Instead of the traditional approach based on compliance minimization the aim of this work is to find a minimum weight structure, which is able to carry a given load while satisfying the condition that the corresponding stresses do not exceed an allowable limit. The general form of the problem is based on the classical limit design formulations of plasticity. The proposed method finds the optimal structure in an iterative way using only stress intensity distribution and does not require from the User explicit knowledge of any gradients or sensitivities. The effectiveness of the proposed methodology has been illustrated on two representative examples including simply supported and cantilever beams.

topology optimization, computational morphogenesis, elastoplastic FE analysis

This paper presents the measurement and model updating of a pedestrian's center of mass trajectory. A mathematical model proposed by the authors is updated using the actual trajectory of a pedestrian. The mathematical model is based on the principle that a human's control capability tries to maintain balance with respect to the pedestrian's center of mass (CoM), independently of the surface type. In this research, the human is considered as a mass point concentrated at CoM. The parameters of the models are updated using experimental identification of the human walking trajectory on a rigid surface. The proposed measurement technique uses a depth sensor, which enable skeletal tracking of the pedestrian walking on rigid or flexible structures. Experiments were performed using a mobile platform with the time-of-flight commercial camera Microsoft Kinect for Windows 2.0. The velocity of the mobile platform is set to maintain a 1 m separation from the pedestrian in order to provide high resolution. The results of the measurement technique allowed the identification of the human's CoM trajectory. The results of the model updating process present the probability density function of the parameters which could be used for modeling the CoM's trajectory of the pedestrian.

Human-structure interaction, Pedestrian's trajectory, Human-induced vibrations, MS Kinect sensor

We present a new human-structure interaction (HSI) model of walking on a flexible surface. A human is considered as a mass point, located at the body’s center of mass (COM). The mass moves along a predefined trajectory, which deforms together with the surface on which the human walks. The forces of motion, equal to the sum of inertial and gravitational forces acting on the mass, are transfered to the surface at prescribed foot positions. The motion of the surface is described using a few selected mode shapes, corresponding damping ratios, and natural frequencies. The equations of motion of the system are time-dependent and discontinuous. They can be written in the form of the second order differential equations of structural dynamics, but with the right-hand forcing dependent on the deformation of the surface. We present a numerical example of a human walking on a long beam structure. The motion of the beam is described by three mode shapes, representing its vertical, lateral, and torsional deflections.

Human induced vibrations, Dynamics of bridges, Human walking model

The purpose of this study is to introduce a new method of damage quantification for truss structures. Its advantage is that it can be directly applied to engineering structures without identifying modal parameters or solving a global optimization problem. The damage is localized and quantified based only on measured acceleration signals, distributed across the structure. Moreover, the method is implemented in a decentralized way rather than a centralized one; that is, for quantification of damage in a given substructure, only a small subset of sensors is considered. The method possesses higher sensitivity to damage than other frequently used methods such as Damage Locating Vectors. Validation of the method has been conducted on a numerical example and a laboratory-scale model of a truss bridge, showing its efficiency and robustness.

structural health monitoring, damage detection, truss structures

This work is focused on experimental verification of existing techniques for localization of a loosened bolted connection. To this end, a laboratory-scale 2-meter-long steel frame is used. The structure consists of 11 steel beams forming a four-bay frame, which is subjected to impact loads using a modal hammer. The accelerations are measured at 20 different locations on the frame, including joints and beam elements. Two states of the structure are considered: a healthy and a damaged one. The damage is introduced by means of loosening two out of three bolts at one of the frame connections. Experimental modal analysis reveals that the loosened bolts in the connection cause a shift only in some of the frame’s natural frequencies, while the others remain insensitive to the damage.

bolted lap connection, frame structure, experimental modal analysis, damage location

The paper deals with a nonlinear analysis of a tall tower, with Circular Flange Bolted Connections (CFBC), in which friction and contact effects are taken into account. Due to these nonlinearities, a detailed dynamic model of the whole structure would lead to very complex computational problem, unable for practical solutions. To overcome these difficulties a reduced order model of CFBC is proposed. Such a model enables the simulation of the whole tower including nonlinearities in connections. The paper is illustrated with an example of model reduction and dynamic calculations for a contemporary telecommunication tower. The tower is assembled of 4 truss segments, of triangular cross section, interconnected with CFBCs. Finally, the influence of the number of modes, included in the reduced order model, on the accuracy and computational effect, is discussed.

Reduced order modeling, Circular flange-bolted connections, Dynamic substructuring, Nonlinear contact and friction effects, Telecommunication towers

Real-time structural health monitoring is very important for truss structures especially those having large-spans. In recent years, many methods have been proposed for damage monitoring of truss structures. However, damage sensitivity of these methods is still required to be improved. In this work an efficient damage localization technique for truss structures is proposed, which is based on the LDLT decomposition of the flexibility difference matrix and the Damage Locating Vectors (DLV) method. Compared with the present Stochastic DLV (SDLV) method, the proposed method is modified in two ways. First of all, the way of calculating the damage locating vectors is modified by using LDLT decomposition instead of Singular Value Decomposition. Secondly, in order to compute the flexibility, the mass matrix which is obtained from the finite element model is used to mass-normalize mode shapes identified from ambient excitations. As a result, the proposed LDLT-DLV method has a higher sensitivity to damage for different types of truss members. The effectiveness of the proposed LDLTDLV method is validated with the numerical example of a laboratory-scale Bailey truss bridge.

Damage localization, damage localization, LDLT-DLV method, truss structure, structural health monitoring

This article presents the implementation of wireless sensors in obtaining modal parameters. The Imote2 platform is used. This is an open platform developed by Intel. The application example is a simply supported wooden plate. It explains how to use the Imote2 sensor and how to extract modal information from the raw data.

wireless sensors, modal analysis

A successful structural monitoring and control systems should be able to discern critical events, scan frequencies and dynamic ranges. This, in turn, requires that models, applied in these systems, are as close as possible to real structural behavior. Many structures, among them, electricity transmission towers, windmills, radio and TV masts, bridges and parabolic dishes, concentrating solar energy, are build as trusses. All of them are subjected dynamic loadings coming, mostly from wind gusts, water waves and thermal activity of sun. The paper is revising assumptions, commonly made for trusses. The main assumption made is that systems of rods are pin joint. Such structures don’t exist, in real engineering design. All, above, mentioned structures are made with rigid or flexible joints. The “pin joint” assumption was made for static analyses. It stated that if joint displacements caused by rod bending can be neglected, comparing with displacements caused by rod elongations, the structural system can be considered as pin joint. As it is commonly known, such cases occur when some necessary conditions joining number of joints and hinges are fulfilled. The “pin joint”, static assumptions has been, without any formal justification, taken for granted in dynamics. Simple examples presented in the paper show that “pin joint” assumption can lead to considerable errors. The paper is illustrated with two numerical examples (simple 2 bar structure and 25 bar transmission tower). Presented examples allowing to compare results of different assumptions applied for structural elements connections.

lattice structures, monitoring, control, structural dynamics

Topics considered in this paper include: dynamic properties of the mast and nonlinearities present in the problem, linearized equations governing guyed mast motion, conditions of stability, contollability and observability. Control forces are exerted by an anchored mechanism in such a way, that they change tension in guy cables. A control algorithm ensuring robust optimal control is also proposed. Finally, the paper is verified by a numerical simulation of a vibration control process.

guyed mast, vibration control

This contribution discusses a semi-active control technique intended for mitigation of structural vibrations. The control law is implemented using the machine learning technique of reinforcement learning, that is in a repeated trial-and-error interaction between the control agent and a simulated environment. Such an approach allows to omit the stage of deriving the optimal control in an analytic way, which is often difficult in nonlinear, semi-actively controlled systems. A specific implementation of the Deep Q Learning (DQN) approach is applied, which promotes control robustness with respect to structural damages. A dedicated network architecture allows the network to be damage-aware, and a specific training procedure involves not only the observations, control actions, and rewards, but also the current health status of the structure.

A numerical example is provided involving a shear-type building model subjected to a seismic excitation. The actuator takes the form of a tuned mass damper (TMD), which is semi-actively controlled by changing the level of viscous damping. The optimally tuned classical passive TMD is used as the baseline reference damping system.

The topic of smart civil infrastructure has attracted significant attention. An important component of such structural systems is the network of sensors used to monitor the structure and deliver information about its current health status. The task of optimal sensor placement is not trivial due to the discrete, combinatorial nature of the problem. The brute force search is unfeasible for large structures, which calls for approximate and heuristic approaches. This problem has been investigated for several decades, beginning probably with the landmark 1978 paper of Shah [1]. A recent review can be found in [2].

The criteria typically used for assessing candidate placements are based either on Kammer’s Effective Independence (EFI) and the Fisher Information Matrix (FIM) [3], and quantify the amount of information provided by sensors, or on covariance matrices obtained within the Kalman filtering procedure used to quantify the uncertainty of the unknown response of interest being estimated [4]. However ingenious, most of the proposed procedures are computationally costly in large-scale problems.

This talk will discuss two optimal placement methods that have been recently developed with the objective of computational efficiency [5, 6]. One of them is based on Kalman filter covariance matrices and has—instead of typically quadratic—a linear complexity in the number of potential sensor locations. The other method uses the technique of convex relaxation to represent the problem in a computationally tractable continuous form and speed up the solution procedure even further. The presented application examples will use models of bridge structures.

[1] P.C. Shah, F.E. Udwadia, A methodology for optimal sensor locations for identification of dynamic systems, J. Appl. Mech. 45(1), 188–196 (1978)
[2] Y. Tan, L. Zhang, Computational methodologies for optimal sensor placement in structural health monitoring: A review, Struct. Health Monit. 19(4), 1287–1308 (2020)
[3] D.C. Kammer, Sensor placement for on-orbit modal identification and correlation of large space structures, J. Guid. Control Dyn. 14(2), 251–259 (1991)
[4] C. Zhang, Y.-L. Xu, Optimal multi-type sensor placement for response and excitation reconstruction, J. Sound Vib. 360, 112–128 (2016)
[5] B. Błachowski, A. Świercz A., M. Ostrowski, P. Tauzowski, P. Olaszek, L. Jankowski, Convex relaxation for efficient sensor layout optimization in large-scale structures subjected to moving loads, Comput.-Aided Civ. Inf. 35(10), 1085–1100 (2020)
[6] B. Błachowski, A. Świercz, P. Olaszek, Ł. Jankowski, Implementation of multi-type sensor placement strategy for large-scale engineering structures, 10th ECCOMAS Thematic Conference on Smart Structures and Materials (SMART 2023), July 3–5, 2023, Patras, Greece, pp. 498–506 (2023)

This study deals with topology optimization of spatial robotic manipulator, the geometry of which was
proposed initially in [1]. The manipulator consists of serially connected modules in a form of a
cylinder cut at a certain angle at its ends. The manipulator constructed in this way allows for relative
rotation of adjacent modules, which gives one degree of freedom per module. The operation of overall
robotic system resembles the elephant trunk manipulator. Previous research involved the possible
kinematic transformations of the manipulator [2], but not its structural optimization [3]. However,
structural design of the involved modules is a challenging task, as the process has to take into account
the current configuration of the module along the manipulator, which results in variable internal force.
It leads to optimization problem under multiple loading conditions with a significantly large number of
loads. This study considers optimal topology of such a modular manipulator structure. Due to the large
variety of possible load conditions, the initial analysis involves a 3D model of the structure with a
continuous set of possible arrangements of individual modules. An additional constraint imposed on
the solution will take into account the symmetry of the optimal topology of a single module, which is
dictated by manufacturing considerations.

optimal topology, modular systems, engineering software

This presentation considers a semi-active control method aimed at the reduction of structural vibrations in the presence of unknown structural damages. The control algorithm is developed using reinforcement learning [1], a machine learning technique characterized by an iterative trial-and-error interaction of the control agent with the controlled structure. A quasi-optimal control law is derived by observing and learning from the collected interaction experience. By being data-driven, this strategy bypasses the need for an analytical derivation of optimal control, which can be challenging in semi-active and nonlinear control systems [2]. The approach of double Deep Q Learning (DQN) with experience replay is used. It builds upon earlier results [3], but here the aim here is to promote control robustness in the presence of unknown structural damages. The control algorithm is ultimately encoded in the form of a trained artificial neural network with a custom architecture that involves a dedicated damage-identification branch.
The effectiveness of the approach is demonstrated using a numerical model of a structure subjected to a seismic-type random excitation. A semi-active tuned mass damper (TMD) is employed as the actuator, and the control signal affects its viscous damping properties. The reference baseline is provided by the optimally tuned, classical passive TMD.

Structural control, Semi-active control, Structural health monitoring (SHM), Reinforcement learning, Machine learning

This contribution reviews a recently proposed semi-active control approach based on the Prestress-Accumulation Release strategy, which aims at damping of structural vibrations by promoting vibration energy transfer from lower- into higher-order modes that have significant material damping. Unlike typical semi-active control, which focuses on local dissipation in actuators, the aim is to trigger natural global damping mechanisms. The actuators are controllable truss-frame nodes: lockable hinges that can change their mode of operation from a frame node (locked hinge) into truss node (free rotation). Sudden removal of such a kinematic constraint releases the accumulated bending energy into high-frequency quickly damped local vibrations. Two formulations are reviewed: decentralized with local-only feedback, and global, which aims at a targeted energy transfer between specific modes. Experimental results confirm the effectiveness using free, forced harmonic and random vibrations.

The aim of the paper is a practical engineering formulation of the topology optimization for
structures made of elastoplastic material. This paper provides a comprehensive approach to
optimizing the topology of elastoplastic structures, including both the problem statement and its
efficient computer implementation. Instead of the traditional compliance minimization approach,
the aim of this work is to find a structure with the minimum mass that can carry on a given load,
provided that the corresponding stresses do not exceed an acceptable limit. The general formulation
of the problem is based on the classical approach allowing to determine the yield strength of the
designed structure [4]. The proposed method finds the optimal structure in an iterative way, using
only the stress intensity distribution and does not require the user to explicitly know sensitivity.

topology optimization, stress constraints, optimal design

In practice, the broadly used finite element (FE) models can have very large number of degrees of freedom (DOFs). A small subset of DOFs representing sensor locations that provides an extremum of a selected objective function corresponding to a metric of the expected measurement accuracy is sought. Thus, optimal sensor placement is characterized by its complex combinatorial nature and tremendous computational effort required. With the aid of convex relaxation, the proposed approach allows one to transform the original combinatorial problem into its continuous counterpart, which requires smaller computational effort – by a few orders of magnitude than famous Effective Independence method. The effectiveness of the method has been demonstrated using an example of a FE model of an existing railway bridge. First, the FE model has been calibrated with measured responses of the bridge under the moving load of a passing train. Then, sensor layout has been obtained in such a way that it optimises the estimate of modal coordinates of the mode shapes participating most significantly in the measured structural response. The authors acknowledge the support of the National Science Centre, Poland (grant agreement 2018/31/B/ST8/03152).

Parametric identification of structures and their components can be encountered in many engineering problems such as damage assessment or model updating for the control purposes. In the present study the attention is on two approaches to model updating. The first approach is the classical penalty func-tion that minimizes the square norm of the error between experimental and numerical modal data. The second one is a probabilistic Bayesian framework that maximizes the a posteriori probability density function of the unknown parameters based on the experimental data. The main difference between these two approaches is related to the fact that the penalty function methods requires matching of the numerical data with those obtained experimentally. The Bayesian approach is not vulnerable to this problem, but it requires more weighting parameters to be selected. An improper selection of these parameters leads to a worse identification accuracy. In this work, the two approaches are compared using data obtained from experiments on a laboratory-scale frame with highly uncertain bolted connec-tions. 17 uncertain stiffness parameters are to be identified: 16 of them correspond to the bolted con-nections and one to the Young modulus of the beams. 82 degrees of freedom are measured with the aid of 4 bidirectional accelerometers and roving sensor technique. Experimental modal data used for model updating contain nine mode shapes and the corresponding natural frequencies within the fre-quency range from 0 to 1 kHz. The research is divided into three steps: (1) model class selection, (2) assessment of the parameter identifiability and (3) updating of the selected model with the aid of both examined model updating methods.

This contribution reviews a recently proposed control strategy for mitigation of vibrations based on the Prestress-Accumulation Release (PAR) approach [1]. The control is executed by means of semi-actively controllable truss-frame nodes. Such nodes have an on/off ability to transfer bending moments: they are able to temporary switch their operational characteristics between the truss-like and the frame-like behaviors. The focus is not on local energy dissipation in the nodes treated as friction dampers, but rather on stimulating the global transfer of vibration energy to high-order modes. Such modes are high-frequency and thus highly dissipative by means of the standard mechanisms of material damping. The transfer is triggered by temporary switches to the truss-like state performed at the moments of a high local bending strain. A sudden removal of a kinematic constraint releases the locally accumulated strain energy into high-frequency and quickly damped vibrations.
The first formulation investigated global control laws [1]. Recent approaches generalized it to decen-tralized control with a local-only feedback, which was tested in damping of free vibrations [2] as well as forced vibrations [3]. Recently, a global formulation was proposed that aims at a targeted energy transfer between specific vibration modes [4], and attempts were made to go beyond skeletal struc-tures [5]. Numerical and experimental results will be presented to confirm the high effectiveness of the approach in mitigation of free, forced random and forced harmonic vibrations.

This contribution concerns a snake-like robotic manipulator arm proposed first in [1]. The manipulator is composed of linearly but nonaxially joined identical modules with a possibility of relative twist, which amounts to one degree of freedom per module. It is an example of an extremely modular system [2], and its advantages are: economization (due to modularity and possible mass production) and robustness (easy repair by replacement of a failed module). The hitherto research involved the possible geometric transformations of the manipulator arm [3], but not its structural optimization. However, structural design of the involved modules is a challenging task, as the process has to take into account the relative position of the module along the arm, as well as the variety of global configurations of the deployed manipulator. It leads to a multi-load structural optimization problem with a significantly large number of loads. This contribution considers topology optimization of such a modular manipulator structure. Due to the large variety of possible load conditions, the initial analysis involves a 2D model of the structure with a discrete set of two possible relative arrangements of adjacent modules. Such a formulation allows the proposed approach to be preliminarily explored, tested and optimized in a numerically manageable simplified environment. The support of the National Science Centre, Poland, granted under the grant agreement 2019/33/B/ST8/02791 is gratefully acknowledged.

To solve the problem of reliability-based topological optimization, a heuristic algorithm was used, consisting in removing redundant material in the areas with the lowest stress intensity. In this algorithm, the design variables represent the material densities in the individual finite elements. The material is removed by reducing the density of finite elements as a function of the stress intensity.

topology optimization, reliability analysis, first order approximation

Despite significant advances in structural health monitoring (SHM), the design of contact sensor networks and their power supply for large-scale structures is still expensive and difficult. Due to the recent progress in computer vision (CV) it is possible to monitor structural components or even whole structures with the aid of digital cameras that allow to avoid the use of the contact sensors. However, CV-based measurements have a significantly lower accuracy than the techniques based on the contact sensors. Moreover, the amount of benchmark data available for development, testing and comparison of CV-based methods is limited. This problem has been partially overcome in recent years by the use of the physics-based graphical models (PBGM) in generation of synthetic but realistic video data. In this work, a comparison of two popular methods of CV-based object tracking applicable in SHM is discussed. PBGM-based videos used in this study are a part of The 2nd International Competition for Structural Health Monitoring'. Exact structural displacements are available due to the fact that PBGM-based video are generated using the structural model. Hence, calculation of the error metrics is straightforward and reliable. The PBGM-based videos show a spatial truss subjected to an unknown excitation.

Nowadays engineering studies require the use of the sophisticated finite element (FE) models consisting of hundreds if not thousands of degrees of freedom. However, using only such models does not allow for accurate reproduction of physical properties of real structures. To overcome this problem usually model updating (MU) techniques are employed. MU usually has one of two goals: 1) modification of some parameters of the model in order to minimize error between output of the FE model and experimental data obtained from the real system, and 2) identification of some properties of the real system using both experimental data and updated FE model. The former case relates to finding the model for performing simulations of the behaviour of the real system. In the later case MU can be applied in damage assessment process. Due to modelling uncertainties minimization of the error between measured and model output does not always provides the most accurate parametric identification. In this research unknown parameters describing rotational stiffness of bolted connections in a frame structure are estimated. Effectiveness of the two competitive model updating methods are compared. The first is based on modal sensitivities and minimizes error between numerical and experimental modal data. It requires matching of the numerical modes with the experimental ones, hence it is often called mode matching. The second is based on probabilistic Bayesian framework. In this approach maximum a posteriori (MAP) estimate of the unknown parameters is searched. It provides an augmented optimization allowing for model updating without mode matching. Moreover, this method is intended for parametric identification and explicitly includes the modelling errors into the problem formulation. In this study vibration modes are obtained from laboratory-scale frame with uncertain bolted connections. It is shown that assembly imperfections have significant influence on the mode shapes of the frame. The results also show that the two methods for model updating provide significantly different values of the identified stiffness parameters for the investigated bolted connections.

In the present study a benchmark test of selected methods of template matching-bated methods for computer vision-based object tracking is performed. The attention is paid to compare these methods in terms of estimation of nodal displacements in a flexible truss structure, aiming at assessment of their reliability in Structural Health Monitoring (SHM) applications. Thanks to the use of synthetic but realistic videos generated with the aid of physics-based graphics models (PBGM), exact displacement of tracked structural nodes are known. Therefore, reliable assessment of the accuracy of the examined methods is possible.

computer vision, structural health monitoring, physics-based graphics models (PBGM)

The uNET neural network architecture has shown very promising results when applied to semantic segmentation of biomedical images. The aim of this work is to check whether this architecture is equally applicable to semantic segmentation distinguishing the structural elements of railway viaducts. Artificial images generated by a computer graphics program rendering the 3D model of the viaduct in a photorealistic manner will be used as data sets. This approach produces a large number of
images that provide a solid training set for machine learning model.

Computer vision, deep learning, semantic segmentation

The goal of the project is the development of methodology for reliable identification of different structural defects, including concrete cracks, spalling and delamination. The basic idea of this project combines machine learning and image processing techniques to localize and quantify stiffness degradation with concrete structures. The overall system is intended to operate in fully autonomous way. it is allowed by recent advancement in image capturing utilizing the unmanned ground or aerial vehicles and artificial intelligence.

structural health monitoring, computer vision, crack detection

Plasticity in topology optimization is almost forgotten direction in this popular research area. This paper presents a recently
developed elasto-plastic topology optimization procedure extended with reliability constraint. It recalls fundamental concepts from
reliability analysis and introduces an algorithm for topology optimization of elasto-plastic structures. In addition to the elasto-plastic
constitutive law of the applied material the optimization algorithm includes stress constraints, as well. The presented numerical examples
show dependence of the volume fraction on probability of failure.

In the present study topology optimization with constraints on the probability of failure is presented. The proposed approach allows controlling the safety level during the optimization process. The number of cycles to structural failure in the case of low-cycle fatigue problem is chosen as a constraint. The low-cycle fatigue requires elastic-plastic formulation of the problem, because in the optimized structure the phenomenon related to accumulation of plastic deformation is observed. In order to estimate the probability of failure for this numerically complex problem, the First Order Reliability Method (FORM) is proposed. The above mentioned methodology is implemented in object-oriented code written in MATLAB programming language.

topology optimization, reliability analysis, low-cycle fatigue, object oriented programming

The paper presents the parametric identification of structural connections characterised by highly uncertain stiffness. Such uncertainties often appear in structural bolted connections. One of the common problems in parametric identification with the use of modal data is the problem of the mode matching. In this work the model updating method based on the Bayesian approach was used to identify the unknown parameters. Due to the probabilistic framework it allows to avoid the problem of the mode matching. A laboratory-scale frame structure is considered in this research, however this structure contains bolted connections common also in large-scale light-weight structures. The problem of parametric identification has been decomposed into the following tasks: (a) selection of the finite element model, (b) evaluation of the identifiability of the parameters, and (c) updating the finite element model with the use of available measurement data.

Bayesian approach, mode matching, system identification, model updating, bolted connections

Structural safety is a critical aspect in modern engineering practice. One of the factors leading to the risk of failure is the variability of design parameters. To be able to estimate the risk of failure, this variability should be taken into account in design process. One way to tackle this issue is to assume a random nature of selected design parameters. These parameters can represent: loads acting on a structure, material properties or shape parameters. Minimizing the structural mass in the process of topology optimization is equivalent to removing the material from the initial, usually regular design space. This process can lead also to a reduction of the structural safety. Therefore, apart from deterministic constraints (such as stresses, displacements or load capacity), it is also worth to control the probabilistic ones. The purpose of this work is to introduce in topology optimization of elastoplastic structures an additional constraint on the probability of failure. Deterministic constraints, in the form of constraints on stresses, are imposed on elastoplastic analysis and utilized by the return mapping algorithm. One of the difficulties coming from the application of these random effects in the process topology optimization is its numerical complexity. Topological optimization itself is a complex issue. Adding a structural safety estimation can extend this process significantly. Fortunately, in the field of reliability analysis, which deals with determining reliability, there are methods that allow for relatively fast estimation of the probability of failure. These are First and Second Order Reliability Methods (FORM, SORM). Only several finite element iterations are sufficient to determine the probability of failure. These methods are based on the concept of the design point or the most probable point. This is the point on the limit state surface that lies closest to the mean point, and represents the most probable failure scenario. Moreover, approximation of limit state surface is linear (FORM) or quadratic (SORM). This allows to estimate quite accurately low probabilities of failure. Such a low probability of failure should characterized a safe structure. The search for a design point is based on the iterative formula developed by Rackwitz and Fiesler. The paper will present the formulation of the elasto-plastic problem of structural analysis as well as the detailed description of the algorithm for topology optimization under reliability constraint. The paper will be illustrated by examples, in which we will demonstrate, how probability of failure changes in the topological optimization process.

topology optimization, elasto-plastic structures, reliability analysis, probabilistic design

W ostatnim czasie wiele prac naukowych poświęcono problemom półaktywnego sterowania drganiami układów mechanicznych. Większość tych prac jednak dotyczy zagadnienia tłumienia drgań, natomiast znacznie mniej z nich obejmuje strategie sterowania na potrzeby odzyskiwania energii z drgających układów. Celem niniejszej pracy jest opracowanie strategii półaktywnego sterowania drganiami, mającej za zadanie przenosić energię drgań wzbudzanych losowo do jednej wybranej postaci drgań własnych. Sterowanie takie realizowane jest przy pomocy dynamicznie rozłączanych węzłów konstrukcyjnych. Węzły w zależności od sygnału sterowania mogą być blokowane w celu przenoszenia momentu zginającego pomiędzy łączonym członami konstrukcji lub odblokowywane, aby pracować jak połączenie przegubowe. Prowadzone badania podstawowe mają wiele potencjalnych zastosowań. Wraz ze zmianą postaci drgań, istnieje możliwość zmiany amplitudy w miejscach, w których zainstalowany jest tłumik lub urządzenie odzyskujące energię (ang. energy-harvester). Możliwe jest również szybkie przeniesienie energii mechanicznej do postaci drgań, która nie zakłóca funkcjonalności konstrukcji lub nie powoduje jej uszkodzenia bądź zmęczenia. W porównaniu do sterowania aktywnego stosowanie sterowania półaktywnego pozwala obniżyć koszty układu, dodatkowo nie powodując destabilizacji konstrukcji [1]. Sterowanie takie może z powodzeniem znaleźć zastosowanie w konstrukcjach o wielu stopniach swobody [2]. Strategia półaktywnego sterowania z użyciem blokowalnych węzłów pierwotnie została opracowana w celu przeniesienia energii drgań do wyższych postaci własnych w celu skutecznej ich redukcji przez tłumienie materiałowe [3]. W niniejszej pracy zaprezentowany zostanie model matematyczny transferu energii oraz oparte na nim prawo sterowania. Dodatkowo przedstawiony zostanie przykład numeryczny pokazujący, że transfer energii mechanicznej jest możliwy nawet wtedy, gdy mierzone są tylko pierwsze – podstawowe – postacie drgań własnych. Prowadzone badania zostały wsparte przez Narodowe Centrum Nauki w ramach projektu Re-Conf (DEC-2017/25/B/ST8/01800).

sterowanie półaktywne, analiza modalna, blokowane węzły

The present study provides a comprehensive framework for sensor layout optimization aiming at accurate estimation of the modal coordinates coming from the structural response. The proposed procedure consists of two steps briefly described below. The first step is a selection of vibrational modes taking part in the motion of structures during their normal operation – in this case subjected to traveling load. Among these structures there are various types of bridges especially railway bridges. In the case of present study structural responses are obtained from rigorous finite element (FE) model of the bridge. The FE model is calibrated with measured response of real bridge located in Huta Zawadzka. The calibration process is based on the displacement signals of the bridge under the traveling load. In the second step modes of interest are selected and a set of candidate sensor locations is proposed. It is a subset of all degrees of freedom (DOFs) of the FE model from which several locations are chosen as best possible locations for the displacement sensors. The above sensor placement problem is a combinatorial task. Many methods for solving such problems have been developed previously, but in the case of large scale structures they require tremendous computational effort. To reduce this effort the so-called convex relaxation is incorporated into optimization process. The technique consists in reformulation of combinatorial problem into continuous convex one. Then, the convex relaxation is achieved by introducing the so-called sensor density function, which assigns a certain metric for individual candidate sensor location. Next, the value of this function is optimized in such a way that it maximize determinant of the Fisher Information Matrix. It has been shown that above algorithm is very effective and is distributing a number of sensors in several iterations only. Finally, it is worth noting that presented method can be used to distribute sensors for structural health monitoring. Moreover, it can be also applied in modal control strategies in vibration suppression.

This study is devoted to a practical method for topology optimization of elastoplastic structures subjected to stress constraints. Instead of the classical compliance minimization problem the aim of this work is to find a minimum weight structure, which is able to carry given load and the corresponding stresses do not exceed an allowable limit. The general form of the problem is based on the classical limit design formulations of plasticity. The proposed method finds optimal structure in an iterative way using only stress intensity distribution and doesn't require computing of any gradients or sensitivities. Our method starts with determining representative stresses in every quadrilateral finite element. At first an elastoplastic analysis is performed to obtain stress values in four Gaussian points, then by the use of von Misses criterion and these stress values the resultant stress is calculated. Next, having obtained stress intensity distribution within the structure we apply penalization to avoid stress concentration issues. Finally, the material is removed proportionally to the stress intensities of individual finite elements. The above mentioned procedure is repeated until limit load capacity is achieved for a given loading vector. The checkerboard problem is solved by means of design filter. Two benchmark problems have been selected as illustrative examples. They are: cantilever and simply supported beam. For these examples parametric studies on different length to height ratios and support patterns are conducted. Additionally, the results of topology optimization for different values of filter radius and penalty parameter are presented.
Finally, efficient computer implementation based on functor-oriented programming is discussed. It is demonstrated how Functor and Template-based programming can be utilized to create versatile Finite Element environment. Within this environment computation of all element matrices and loading vectors can be called in the same way, this in turn allows for implementation of effective aggregation procedure.

topology optimization, minimum-weight design, functor-oriented programming, stress constraints

The subject of this study is an efficient approach to the development of a finite element framework, which is intended to be used for solving a variety of problems in computational solid mechanics. One of such problems, recently becoming an active field of research, is topology optimization of structures made of elastic-plastic materials. For finding the optimal topology of real, practical and complex structures the knowledge of a number of numerical algorithms is required, to mention a few: modification of finite element meshes, aggregation of tangent stiffness matrices, or direct and iterative solvers. The classical computer implementation of the original Classical Optimality Criteria method (COC) of the topology optimization problem given by Bendsoe and Sigmund is relatively simple and contains 99 lines of code in the MATLAB language. However, it assumes that there exists only a single loading case, single displacement (compliance) constraint, the material is linearly elastic and the optimal topology can be found using the so-called Solid Isotropic Material with Penalization (SIMP) algorithm, which is based on the original COC method. In reality, engineers face a slightly different problem. They need to find the topology of a minimum weight structure subjected to multiple loading cases, made of an elasto-plastic material, and with a limit on stresses. The above mentioned SIMP approach may not lead to an optimal solution.

functor-oriented programming, topology optimization, elastoplastic FE analysis

The vibration attenuation problem has been solved using many different methods, some of which involve the use of advanced control algorithms. The topic of harvesting the energy of structural vibrations is less explored. For that reason, this contribution studies the problem of conversion of mechanical energy of vibrations. The paper presents a method of semi-active control, which is applied to dynamically transfer the vibration energy into a selected vibration mode. The target mode is selected in such a way that the amount of energy that can be recovered during the vibration process is maximized. In other words, switching between two modes is not intended to dissipate the energy of vibrations, but rather to maximize the energy-harvesting potential of the overall system. The concept will be illustrated using an example of a simple frame structure, in which semi-actively controlled lockable joints modify the modal properties of the structure.

semi-active control, lockable joints, energy-harvesting

Classical programming of finite elements contains usual class, which duty is not only to approximate some physical field of interest (displacements, accelerations or temperature), but also definition of matrices necessary for particular analysis. It often leads to sophisticated class hierarchy of finite elements. In our approach matrices necessary for FE analysis are in separate classes. Hierarchy of these classes can be developed almost separately from declaration of the finite element class. Also finite elements hierarchy is much smaller, because each class represents one kind of matrix computed in FE analysis. In our opinion the functor is best suited object for this kind of approach. The functor represents one subroutine and it can also be invoked as function. The study presents application of functor oriented programming to finite element analysis.

stress constrained topology optimization, finite element programming, functor-oriented implemenetation

The purpose of this study is the mechanism of the spatial movement of a human during walking. The human is considered to be a rigid body with six degrees of freedom, and its mobility is reduced by two constraints. One of the constraints is related to an assumption of constant length of the leg, foot of which is moving along given straight line. The second constraint corresponds to an assumption that human's centre of mass can move only in vertical plane. The dynamic model of the mechanism is built under above assumptions connected to the human gait kinematics. Then, kinetic energy function is derived. In the next step of the study the muscle force in the stance leg, together with its potential, is discussed. It is assumed that this force is piecewise-linear, which can be reasonably approximated by a cubic polynomial. For that purpose a smoothing procedure is proposed and finally with the aid of the Lagrange function dynamic equations for the 3D human gait are formulated. The last part of the paper is devoted to the numerical solution of obtained nonlinear equations, arising from the Lagrange procedure.

human walking, gait analysis, lagrangian dynamics

A substructuring method for the prediction of the dynamic response of footbridges subjected to loadings induced by a pedestrian is presented. The dynamic system is composed of two independent subsystems. The first one is the model of the suspension footbridge, and the second one is the model of a pedestrian. The former is obtained using the standard finite element method, while the latter is created by applying a two-step identification approach. The first step is an inverse kinematics based on an experimental human motion analysis. The second one relies on Proper Orthogonal Decomposition extracting a number of most important modes, describing the motion of the pedestrian. The presented methodology will be demonstrated by a numerical example of the pedestrian-footbridge interaction.

dynamic substructuring, human-structure interaction, suspension footbridges

A relatively simple method of finding discrete minimum structural weight is proposed. It is based on a tree graph, representing discrete values of the structural volume. In the proposed method, the number of analyses is limited to the order of two. The paper is illustrated with an example containing up to 42 to the power 38 combinations.

structural optimization, problem oriented optimization, discrete optimization, combinatorial optimization, graphs, structural static and dynamic analyses, time domain, frequency domain

The paper is illustrated with numerical examples of two bar and 25 bar tower structures. Results of different assumptions, applied to the structural elements connections are discussed.

Transmission towers, monitoring of structures

In this study, the idea of removing redundant material is enhanced by combining the continuous and discrete solutions. At the end of the paper, several numerical examples, with numbers of combinations up to 308 are presented and their effectiveness is validated.

discrete optimization, removing redundant material

The objective of this paper is a numerical simulation of vibration control of a mast supported by tendons. This problem requires knowledge from many different disciplines such as multibody dynamics, control theory and numerical methods.

vibration control, wind disturbances