Institute of Fundamental Technological Research

We present a nonlinear finite element analysis to investigate the buckling and post-buckling behaviour of functionally graded material (FGM) plates resting on the elastic foundation. The material properties are assumed to vary gradually across the thickness according to a power law distribution. The starting point of the investigation is the generalized third-order plate theory and the Vlasov model of elastic foundation having properties varying throughout the depth. The plates are subjected to bending to verify the formulation and compression loads including buckling and post-buckling analysis to investigate the influence of various parameters on the structural response. Key words: FGM plate, elastic foundation, post-buckling, nonlinear finite element analysis.

FGM plate, elastic foundation, post-buckling, nonlinear finite element analysis.

sztuczna inteligencja,globalne zagrożenia,interfejs mózg-komputer,potrzeba globalnych regulacji

współpraca,mobilność studentów,synergia wyników badań,wspólne dyplomy

We present a nonlinear finite element analysis to investigate the nonlinear behaviour of functionally graded materials (FGM) plates. The material properties are assumed to vary gradually across the thickness according to a power law distribution. The starting point of the investigation is the generalized third-order plate theory which is modified in the present analysis to include the position of the neutral surface and enhanced with additional terms to represent the distribution stresses better. The plates are subjected to bending and compression loads including buckling and post-buckling analysis.

FGM plate, Nonlinear finite element analysis, Bending, Post-buckling

In this paper, some of the displacement-based plate theories are used to investigate the elastic-plastic analysis of plates in the framework of the finite element method including the buckling and postbuckling effects with the focus on the general third-order plate theory (GTPT). The plate calculation results were compared with the results obtained using 64-nodes solid elements involving Lobatto integration scheme. The problem is solved using the Newton–Raphson method applying modified Crisfield constant arc-length procedure. The results show good agreement of results and the GTPT can be acknowledged to fulfill essential criteria for application to the elastic-plastic analysis of thin and thick plates.

buckling and postbuckling, elasto-plastic plates, third-order plate theory

High pressure variable displacement axial piston pumps are subject to complex dynamic phenomena. Their analysis is difficult, additionally complicated by leakage of the working fluid. Analytically gap flow is calculated with the Reynolds equation which describes the pressure distribution in a thin lubricating layer. The paper presents various approaches to analyze gap flow both in traditional axial piston pump and novel type of hydraulic pump, designed at the Polish Gdansk Institute of Technology. Because of large aspect ratio between the height of the gap and the size of pump elements, the authors present the numerical simulation approach using a local model to define a lubrication gap, linked to a global model of a pump from which boundary conditions were imported. User defined functions implemented in Fluent and Excel were used to calculate the pressure and velocity fields and assess the fluid flow rate.

We present a nonlinear finite element method to investigate the nonlinear stability of stiffened functionally graded materials (FGM) plates considered as a whole unit. The plates are subjected to mechanical and thermal loads. The material properties are assumed to be temperature dependent and varied gradually across the thickness according to a power law distribution. The nonlinear equations of FGM plates are based on the first-order shear order plate theory. The influence of material, geometrical properties of stiffeners and initial deflections on the buckling and post-buckling response of the stiffened plates are studied in detail. Including the latest information no work has been oriented towards post-buckling analysis of stiffened FGM plates considered as a whole unit.

FGM stiffened plate, nonlinear finite element analysis, post-buckling

The geometrically nonlinear free vibration of functionally graded thick plates resting on the elastic Pasternak foundation is investigated. The motion equations are derived applying the Hamilton principle. We consider the first order shear deformation plate theory (FSDT), in which the modified shear correction factor is required. A 16-noded Mindlin plate element of the Lagrange family which is free from shear locking due to small thickness of the plate used. The material properties are assumed to be temperature-dependent and expressed as a nonlinear function of temperature. Because the FGM plates are not homogeneous, the basic equations are calculated in the equivalent physical neutral surface which differs from the geometric mid-plane. In the pre-buckling range natural frequencies decrease ultimately reaching zero for critical stress in the bifurcation point.

FGM plates, Two-parameter elastic foundation, Nonlinear free vibration, Finite element method

The aim of the present study is to provide a methodology for improving the design of a shrink-fitted assembly by focusing on two objectives: (i) taking into account the surface roughness of components, (ii) introducing a non-classical hardening friction law in which tangential micro-slip displacements are considered. The calculations have been made for elasto-plastic properties of component in axisymmetric conditions. Both the loading and unloading processes have been considered. After finite element simulations, it is observed that overall static behaviour of the assembly is influenced considerably by the surface finish of the mating components. The current numerical results of the shrink fitted assembly received from the coarse mesh could be treated as contact benchmark for further finite element analyses using as closely as possible identical input data.

Shrink-fit, Roughness, Finite elements, Elasto-plasticity

First, we discuss characteristics of functionally graded materials and describe methods of their manufacturing. Then, we provide an overview of analytical and numerical methods for calculating plates, with characteristics of functionally graded materials, resting on elastic foundation. The presented numerical results have been obtained by the finite elements method, referring to post-bifurcation problems of thermally loaded plates. The first-order shear deformation theory (FSDT) has been employed. In numerical calculations we have used a new 16-node plate element, free of problems related to shear locking.

Thick plates, Functionally graded materials, Finite elements method

The Pasternak elastic foundation model is employed to study the statics and natural frequencies of thick plates in the framework of the finite element method. A new 16-node Mindlin plate element of the Lagrange family and a 32-node zero-thickness interface element representing the response of the foundation are used in the analysis. The plate element avoids ill-conditioned behaviour due to its small thickness. In the case of the eigenvalue analysis, the equation of motion is derived by applying the Hamilton principle involving the variation of the kinetic and potential energy of the plate and foundation. Regarding the plate, the firstorder shear deformation theory is used. By employing the Lobatto numerical integration in which the integration points coincide with the element nodes, we obtain the diagonal form of the mass matrix of the plate. In practice, diagonal mass matrices are often employed due to their very attractive timeintegration schemes in explicit dynamic methods in which the inversion of the effective stiffness matrix as a linear combination of the damping and mass matrices is required. The numerical results of our analysis are verified using thin element based on the classical Kirchhoff theory and 16-node thick plate elements.

Mindlin plate, two-parameter elastic foundation, Lobatto integration, bending and eigenvalue analysis

A review of findings contained in the IPCC AR5 Synthesis Report, of particular relevance to the Polish audience, is offered. Polish perspectives on coal-climate nexus are discussed in a broader, universal, context. Positive examples of climate policies in other countries are provided. The title of this paper refers to a public conference organized in Warsaw by the Embassies of France, Germany, and the UK and the Polish Academy of Sciences.

climate change, climate change mitigation, IPCC, coal-climate nexus in Poland

We used the fractal theory based on a single variable Weierstrass–Mandelbrot function to obtain the normal contact stiffness if rough and smooth isotropic surfaces are pressed against each other. Because in the original fractal theory the distribution of contact area is assumed geometrically, we propose the method in which the actual deformation of asperities and a correction due to asperity coupling (interaction) will be taken into account. This correction is equivalent to an increase of the effective separation by a quantity proportional to the nominal pressure and it has a significant effect on contact stiffness at larger normal loads (low separations). The numerical results demonstrate a nonlinear evolution of the contact stiffness with the normal load in particular in the first stage of loading at low squeezing pressures. We have compared the results of the theoretical contact stiffness using the fractal method with the experimental ultrasonic measurements. Experimental results made on real surfaces agree remarkably well with the theoretical predictions.

fractal model, contact stiffness, ultrasonic measurements

Poziom nauki i kompetencje technologiczne kluczowych instytucji i firm są istotnym elementem bezpieczeństwa państwa. Niezwykle ważne jest więc przemyślane skoordynowanie działalności całego krajowego sektora badań i innowacji z narodową strategią bezpieczeństwa. Szczególną rolę w ustalaniu priorytetów i finansowaniu badań naukowych w naszym kraju ma dzisiaj Unia Europejska. Dlatego specjalną uwagę należy zwrócić na politykę wspomagania naszego udziału w wiodącym programie badawczym Unii, czyli w Horyzoncie 2020. Oferuje on wiele możliwości wzmocnienia naszych instytucjonalnych kompetencji naukowo-badawczych związanych z szeroko rozumianym bezpieczeństwem, co w powiązaniu z już istniejącym, znaczącym potencjałem naszych ośrodków badawczych stanowi wielką szansę na trwałe wzmocnienie naszych zdolności w tym zakresie.

The present study is divided in two parts. In the first one the complete elasto-plastic microcontact model of anisotropic rough surfaces is given. Rough surfaces are modelled as a random process in which the height of the surface is considered to be a two-dimensional random variable. It is assumed that the surface is statistically homogeneous. The description of anisotropic random surfaces is concentrated on strongly rough surfaces; for such surfaces the summits are represented by highly eccentric elliptic paraboloids. The model is based on the volume conservation of asperities with the plasticity index modified to suit more general geometric contact shapes during plastic deformation process. This model is utilized to determine the total contact area, contact load and contact stiffness which are a combination of the elastic, elasto-plastic and plastic components. The elastic and elastoplastic stiffness coefficients decrease with increasing variance of the surface height about the mean plane. The standard deviation of slopes and standard deviation of curvatures have no observable effects on the normal contact stiffness. The part two deals with the solution of the fully three-dimensional contact/friction problem taking into account contact stiffnesses in the normal and tangential directions. An incremental non-associated hardening friction law model analogous to the classical theory of plasticity is used. Two numerical examples are selected to show applicability of the method proposed.

The complete elasto-plastic microcontact model of anisotropic rough surfaces is proposed. The description of anisotropic random surfaces is restricted here to strongly rough surfaces; for such surfaces the summits are represented by highly eccentric elliptic paraboloids having their semi-major axes oriented in the direction of the grain. The present model is based on the volume conservation of asperities in which the plasticity index is modified to suit more general geometric contact shapes during plastic deformation process. This model is utilized to determine the total contact area, contact load and contact stiffness which are a mixture of both the elastic and plastic components. For low nominal pressures both the elastic and elasto-plastic contact stiffness is found to be almost linear in relation to the normal load. The elastic and elasto-plastic stiffness coefficients decrease with increasing variance of the surface height about the mean plane. The standard deviation of slopes and standard deviation of curvatures have no observable effects on the normal contact stiffness.

Rough surfaces, Statistical modelling, Contact stiffness, Finite element method

Gradient-based optimization methods are still most efficient methods for solving structural optimization problems. The sensitivity formulation has been one of the central issues in the gradient-based optimization algorithm. Thermo-viscoelastic constitutive and parameter sensitivity formulation are presented in this paper. The model considered is composed of two coupled subproblems: the transient heat transfer problem and a rheological, viscoelastic material model known in literature as the standard model. Design variables considered are with material and shape-defining parameters. The investigation includes a finite element formulation and implementation in an object-oriented finite element environment. Results of numerical analysis are presented.

Finite element method, Sensitivity analysis, Viscoelasticity

W artykule przedstawiono sposób postępowania podczas szacowania niezawodnoÊci dużych nieliniowych układów konstrukcyjnych. Nacisk położono na zastosowanie metody różniczkowania bezpośredniego (DDM). Jako przykład wybrano żelbetową konstrukcję budynku osłonowego reaktora nuklearnego.

inżynieria nuklearna, niezawodność, analiza wrażliwości, konstrukcje żelbetowe

Computational time needed for reliability abalysis of realistic structural problems as a rule is very high. Improvements in efficiency are critical to allow solution of large realistic problems. The realiability analysis is usually performed using approximate First Order Reliability Method (FORM). Iterative solution procedures of FORM require extensive design sensitivity computations of high accuracy. The design of realistic structures requires computer-based numerical procedures, such as finite element analysis. The design sensitivity gradients are not explicitly available in terms of design variables. The most intensive computational task of design sensitivity computation should be carried out by highly efficient and accurate methods such as discrete design sensitivity analysis, This paper describes requirements for design sensitivity information for reliability analysis. The way of coupling reliability computationa with discrete AVM and DDM methods of design sensitivity analysis is pointed out. A computational program developed for layered concrete shells allows one to solve large realistic reliability problems. The reliability study of an RC nuclear containment shell is carried out. Reliability studies show which pf mthe parameters have the highest impact on the reliability of the vessel.

Nuclear engineering, reliability, design sensitivity, FEM

An algorithm for design sensitivity analysis of elasto-plastic response for the case of design-dependent geometry is discussed. The domain parametrization approach is employed. Some important implications for the concept of isoparametric element formulation are indicated. The idea of shape sensitivity computations is similar to that of sensitivity with respect to material parameters. However, derivation of additional geometric matrices and integral expressions is necessary. A possible discontinuity of sensitivity solutions is indicated and it is shown that the algorithm handles it correctly. A plane stress computational example illustrates the application of the method.

Development of computational models for plane stress elasto-plasticity is known to make some difficulties non-existent in 3D and plane strain formulations. Tedious derivation of plane stress algorithmic tangent matrices which cannot be directly obtained as a special case of 3D matrices may serve here as an example. In this paper specific features of plane stress computations are discussed in the context of parameter sensitivity analysis. Elasto-plastic material model with isotropic/kinematic hardening as well as two viscoplastic models are considered. Explicit expressions for sensitivity gradients are derived. Instructive examples solved by FEM illustrate the paper.

A simple element to model frictional contact in steady state metal forming processes is presented together with the sensitivity analysis to the friction coefficient in a Coulomb friction law. The interest of such model arises from the analysis of rolling processes and a two dimensional approach to cutting problems, where the contact zone is to be determined, however a stationary state is present in most part of the operation. The flow approach proves to be an adequate method to handle efficiently this situation. The contact elements impose a restriction in the velocity component normal to the boundary and a tangential friction force opposite to the velocity. The parts of the boundary which are not in closed contact are treated as free surfaces, which must fulfill the condition of being streamlines. Sensitivity analysis with respect to the friction coefficient is performed by the Direct Differentiation Method (DDM). The effect of variations in this parameter is discussed for the simulation of an extrusion and a cutting problem.

Computer simulation, Extrusion, Friction, Metal cutting, Rolling, Sensitivity analysis, Contact zone, Coulomb friction law, Direct differentiation method, Flow approach, Friction coefficient, Frictional contact, Steady state metal forming processes, Metal forming

The flow formulation for metal forming analysis based on a rigid-viscoplastic material rncdel is considered. Specifically, sensitivity evaluation techniques are discussed for different solution variables with respect to variations in parameters entering the constitutive (and other) equations such as material constants, imposed velocities or friction coefficient. A method to avoid spurious pressure modes is introduced which allows to use Ql/Ql elements and thus to accurately calculate pressures, their sensitivities and friction forces. In addition, one pressure unknown for each node is available in this method, thus yielding a finer discretisation for this variable.

Computer aided analysis, Friction, Sensitivity analysis, Velocity, Viscoelasticity, Metal forming processes, Parameter sensitivity, Metal forming

Shape sensitivity analysis is presented for metal-forming processes described in terms of the flow approach [1]. The direct differentiation method is employed to derive the sensitivity expressions. The continuum approach is adopted so that both the equilibrium equations and response functional are differentiated before discretization. The necessary derivatives with respect to shape design variables are calculated making use of the framework already available for isoparametric elements (control volume approach). In finite element implementation a system of equations is obtained which has the same system matrix as the equilibrium problem. The right-hand side is calculated by partially differentiating the internal and external forces with respect to the design parameters. The procedure is illustrated by calculating sensitivities of some independent and dependent variables with respect to the die angle in an extrusion problem and to the roll radius in a plane rolling.

Calculations, Continuum mechanics, Differentiation (calculus), Finite element method, Matrix algebra, Metal extrusion, Metal forming, Rolling, Die angle, Direct differentiation method, Discretization, Equilibrium equations, Response functional, Roll radius, Shape sensitivity analysis, Sensitivity analysis

The paper presents equations and algorithms for numerical computation of elasto-plastic and elasto-viscoplastic constitutive parameter sensitivity problems. The general integration idea is based on the return-mapping algorithm. Two viscoplastic constitutive models are discussed in details: the overstress (Perzyna) model and the power law strain and strain-rate hardening model. The use of the consistent tangent operator is shown to be essential for the accuracy of the sensitivity analysis. A possible discontinuity of sensitivity at the transition (yield limit) point is discussed. It is concluded that in principle the nonuniqueness of the sensitivity solutions at such points does not invalidate the general idea of sensitivity calculations. A number of numerical examples illustrate the theoretical considerations.

Sensitivity Analysis, Numerical Computation, Constitutive Model, General Idea, Theoretical Consideration

The general problem of sizing, material and loading parameter sensitivity of non‐linear systems is presented. Both kinematic and path‐dependent material non‐linearities are considered; non‐linear sensitivity path is traced by an incremental solution strategy. The variational approach employed is quite general and can be employed for studying sensitivity of various path‐dependent highly non‐linear phenomena. Both the direct differentiation method (DDM) and adjoint system method (ASM) are discussed in the context of continuum and finite element mechanics. The merits of using the consistent tangent matrix and the necessity of accumulation of design derivatives of stresses and internal parameters are indicated. Aspects of sensitivity problems in metal forming are also discussed. A number of examples illustrate the paper.

Direct differentiation method, Adjoint system method, Metal forming

A complete mechanical model of lungs, valid for the analysis of stresses in tissues, which considers mechanical couplings between the tissue deformation and the air flow, is presented. The concept of a continuous description of the lung is adopted, with its volume assumed to be filled with a nonlinearly elastic, highly deformable solid - parenchyma, which is a thin-walled porous tissue structure on the micro-scale. Central airways are modelled as a discrete system of conduits immersed in the parenchyma. For the flow in peripheral airways and alveoli, a model of filtration in a three-dimensional two-phase porous medium (gas-tissue skeleton) is assumed. A new approach to pseudoelastic nonlinear constitutive modelling of parenchyma aiming at computational applications is presented. A fundamental set of nonlinear differential equations for the quasi-static coupled problem is derived and frictionless contact boundary conditions are included. A finite element formulation of the problem with an implicit time integration scheme is presented. The results of numerical examples obtained using the algorithm agree qualitatively with experimental data.

parenchyma

Finite element formulations for structural sensitivity analysis of non‐linear systems with fixed overall shape are discussed. Both the direct differentiation and adjoint variable methods are employed. The resulting sensitivity algorithms are consistent with time integration scheme adopted for solving equilibrium problem. Effectiveness and computational aspects of the procedures are discussed and compared. Numerical algorithms are shown to be readily implemented in existing finite element codes. Large‐scale examples illustrate the paper.

sensitivity analysis, nonlinear systems, incremental approach, finite element method

A method is presented for modifying the triangular factors of the global stiffness matrix with nonsymmetric stiffness modifications. The proposed procedure is based on the Bennett's algorithm and applies to nonlinear structural analysis by the finite element method. The appropriate computational cost analysis is included and states the conditions of the economical use of the method.

Full limit analysis is preseted of a thin plate under plane stress, perforated with circular holes arranged in a regular penetration pattern. The material is assumed to be elastic–perfectly plastic and to obey the Huber–Mises yield condition together with its associated flow law. The finite element tangential stiffness method is employed. Triangular constant-strain elements are used, the load being generated by means of constant edge displacements at the periphery of a suitably selected subregion. Load-displacement diagrams are obtained for various edge displacement programs and then an interaction curve is constructed for the perforated plate considered. Each computational step is associated with a certain plastic zone which develops until the limit state configuration is reached. The plate is provided with equilateral triangular configuration of holes with arbitrary cutout coefficients. The interaction curves are plotted against the Huber–Mises yield condition for the plate without openings.

Some aspects of the analysis of elastic-plastic deformation processes with both elastic and plastic finite strain components are studied. The discussion is intentionally restricted to the geometric description of such situation. As a starting point the intermediate configuration concept is accepted but some important generalizations to it appear to be necessary. Basing upon this concept the properly invariant forms of strain and rate of strain measures are defined being referred to the the reference, intermediate and actual configurations, respectively. The applicability of the different strain measures to the constitutive equations is discussed.

This paper deals with the design sensitivity of structural systems giving an outline of a sensitivity algorithm for RC structures. As an examples, an RC nuclear containment vessel is chosen. The linear and nonlinear analyses are performed.

parameter sensitivity, nonlinear analysis, reinforced structures, nuclear containment vessels

The paper presents a reliability problem of a nuclear containment vessel. The reliability problem is solved with an application of parameter sensitivity analysis. It is a layered concrete shell structure. The failure function depends on a displacement constraint.

reliability analysis, parameter sensitivity, reinforced concrete, nuclear containment vessel

An incremental formulation based on the Taylor's expansion for nonlinear design sensitivity problems is developed. Computational aspects are discussed. A few numerical benchmark problems illustrate the paper.

design sensitivity, nonlinear geometry, incremental procedure

parameter sensitivity, plate-shell structures, nonlinear analysis