Partner: Ewa Turska, PhD, DSc |
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Doctoral thesis
1990 | O lokalnym uplastycznieniu otoczenia wierzchołka szczeliny w antypłaskim stanie odkształcenia
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Habilitation thesis
2015-10-29 | Zbieżność i stabilność algorytmów numerycznych w sformułowaniach wielopolowych mechaniki |
Recent publications
1. | Wiśniewski K., Turska E.♦, Reduced representations of assumed fields for Hu–Washizu solid-shell element, COMPUTATIONAL MECHANICS, ISSN: 0178-7675, DOI: 10.1007/s00466-023-02275-1, Vol.71, pp.957-990, 2023 Abstract: Mixed eight-node (hexahedron) solid-shell elements based on the standard or partial version of the three-field Hu–Washizu (HW) functionals are developed for Green strain. Three reduced representations of the assumed stress/strain fields are selected. They improve effectiveness, yet retaining good accuracy and convergence properties. At the outset, the standard HW functional and the assumed stress/strain representations of the 3D solid element B8-15P (Weissman in Int J Numer Methods Eng 39:2337–2361, 1996) are used to derive a solid-shell element with 51 parameters. To eliminate locking, the ANS method is applied to the thickness strain (Betsch and Stein in Commun Numer Methods Eng 11:899–909, 1995) and to the transverse shear strain (Dvorkin and Bathe in Eng Comput 1:77–88, 1984). It is a correct element which, however, yields too large displacements for coarse meshes and trapezoidal through-thickness shapes. To improve the above formulation, the ζ-independent reduced representations of the assumed stress/ strain fields are selected and the transformations to Cartesian components are modified. The thickness strain is enhanced by the EAS method. The element with 35 parameters is derived from the standard/enhanced HW functional, but, to further reduce the assumed fields, partial/enhanced HW functionals are constructed from the 3D potential energy by applying the Lagrange multiplier method only to selected strain components. In the element with 27 parameters, this is applied to the constant in-plane strain and to the transverse shear strain while in the element with 19 parameters, to the constant in-plane strain only.Two other modifications are implemented to enhance the behavior of these elements: (A) the skew coordinates are used in the reduced representations of the in-plane stress/strain (Wisniewski and Turska in Int J Numer Methods Eng 90:506–536, 2012), and (B) the Residual Bending Flexibility correction of the transverse shear stiffness (MacNeal in Comput Struct 8(2):175–183, 1978) is adapted. Finally, the performance of the proposed solid-shell HW elements is demonstrated on several linear and non-linear examples for the linear elastic material and the hyper-elastic material. The proposed elements are compared to each other and to the best existing elements of this class. Keywords:Eight-node (hexahedron) solid-shell elements , Standard or partial Hu–Washizu functionals, Reduced representations of assumed stress/strain , RBF correction Affiliations:
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2. | Wiśniewski K., Turska E.♦, Improved nine-node shell element MITC9i with reduced distortion sensitivity, COMPUTATIONAL MECHANICS, ISSN: 0178-7675, DOI: 10.1007/s00466-017-1510-4, Vol.62, No.3, pp.499-523, 2018 Abstract: The 9-node quadrilateral shell element MITC9i is developed for the Reissner-Mindlin shell inematics, the extended potential energy and Green strain. The following features of its formulation ensure an improved behavior: 1. The MITC technique is used to avoid locking, and we propose improved ransformations for bending and transverse shear strains, which render that all patch tests are passed for the regular mesh, i.e. with straight element sides and middle positions of midside nodes and a central node. 2. To reduce shape distortion effects, the so-called corrected shape functions of Celia and Gray (Int J Numer Meth Eng 20:1447–1459, 1984) are extended to shells and used instead of the standard ones. In effect, all patch tests are passed additionally for shifts of the midside nodes along straight element sides and for arbitrary shifts of the central node. 3. Several extensions of the corrected shape functions are proposed to enable computations of non-flat shells. In particular, a criterion is put forward to determine the shift parameters associated with the central node for non-flat elements. Additionally, the method is presented to construct a parabolic side for a shifted midside node, which improves accuracy for symmetric curved edges. Drilling rotations are included by using the drilling Rotation Constraint equation, in a way consistent with the additive/multiplicative rotation update scheme for large rotations. We show that the corrected shape functions reduce the sensitivity of the solution to the regularization parameter γ of the penalty method for this constraint. The MITC9i shell element is subjected to a range of linear and non-linear tests to show passing the patch tests, the absence of locking, very good accuracy and insensitivity to node shifts. It favorably compares to several other tested 9-node elements. Keywords:9-node shell element MITC9i, Two-level approximation of strains, Patch tests, Corrected shape functions, Node shift parameters, Coarse mesh accuracy, Drilling rotations Affiliations:
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3. | Panasz P., Wiśniewski K., Turska E.♦, Reduction of mesh distortion effects for nine-node elements using corrected shape functions, FINITE ELEMENTS IN ANALYSIS AND DESIGN, ISSN: 0168-874X, DOI: 10.1016/j.finel.2012.11.003, Vol.66, pp.83-95, 2013 Abstract: The paper concerns two-dimensional nine-node quadrilateral elements based on the Green strain and the two-level approximations of strains. These approximations reduce locking well for regular meshes but cannot prevent the drop of accuracy when the side and central nodes are shifted from the middle positions. Two-dimensional nine-node elements, Corrected shape functions, Two-level approximations of strains, Patch tests, Shape distortions Affiliations:
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4. | Wiśniewski K., Turska E.♦, Four-node mixed Hu-Washizu shell element with drilling rotation, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.3335, Vol.90, pp.506-536, 2012 Abstract: In this paper, enhanced four-node shell elements with six DOFs/node based on the Hu–Washizu (HW) functional are developed for Green strain. The drilling rotation is included through the drilling rotation constraint equation. The key features of the approach are as follows. four-node mixed shell element with six DOFs/node, pure or partial Hu–Washizu functionals, drilling rotation, optimal representations, skew coordinates Affiliations:
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5. | Wiśniewski K., Wagner W.♦, Turska E.♦, Gruttmann F.♦, Four-node Hu-Washizu elements based on skew coordinates and contravariant assumed strain, COMPUTERS AND STRUCTURES, ISSN: 0045-7949, DOI: 10.1016/j.compstruc.2010.07.008, Vol.88, pp.1278-1284, 2010 Abstract: Mixed 4-node elements based on the Hu–Washizu (HW) functional are developed for the representation of the assumed strain in the natural basis at the element’s center, i.e. for the contravariant transformation rule. In other aspects, the formulation is identical as in our previous paper [9], to which this note is an addendum. Four-node finite elements, Hu–Washizu functional, Plane stress, Mixed elements, Skew coordinates, Contravariant assumed strain Affiliations:
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6. | Wiśniewski K., Turska E.♦, Improved four-node Hu-Washizu elements based on skew coordinates, COMPUTERS AND STRUCTURES, ISSN: 0045-7949, DOI: 10.1016/j.compstruc.2009.01.011, Vol.87, pp.407-424, 2009 Abstract: Mixed 4-node elements based on the Hu–Washizu (HW) functional are developed for stress and strain representations in various coordinates, including the skew, natural and Cartesian ones. The HW functional is used in incremental form, suitable for non-linear materials. The key features of our approach are as follows. 4-Node finite elements, Plane stress, Incremental Hu–Washizu functional, Mixed elements, Mixed/enhanced elements, Skew coordinates Affiliations:
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7. | Wiśniewski K., Turska E.♦, Improved four-node Hellinger-Reissner elements based on skew coordinates, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.2343, Vol.76, pp.798-836, 2008 Abstract: Mixed four-node elements based on the Hellinger–Reissner (HR) functional are developed for stress representations in various coordinates, including the skew, natural and Cartesian ones. The two-field HR functional is used in the classical form and in the incremental form suitable for non-linear materials. four-node finite elements, incremental Hellinger–Reissner functional, assumed stress element, assumed stress/enhanced strain element, skew coordinates Affiliations:
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8. | Wiśniewski K., Kowalczyk P., Turska E., Analytical DSA for explicit dynamics of elastic-plastic shells, COMPUTATIONAL MECHANICS, ISSN: 0178-7675, DOI: 10.1007/s00466-006-0068-3, Vol.39, No.6, pp.761-785, 2007 Abstract: The paper presents an analytical constitutive design sensitivity analysis (DSA) algorithm for explicit dynamics of elastic-plastic finite rotation shells. Two explicit dynamical algorithms for finite rotation shells are presented, and the DSA is developed for the one formulated in terms of the rotation vector and its time derivatives, {ψ,ψ˙,ψ¨}. The hypo-elastic constitutive model based on the Green-McInnis-Naghdi stress rate is used to derive an incremental algorithm in terms of ‘back-rotated’ objects. The associative deviatoric Huber-Mises plasticity modified by plane stress conditions is implemented in the form suitable for finite rotation/small elastic strain increments. The analytical DSA is developed for the above-specified problem, with the design derivatives calculated w.r.t. material parameters. Design-differentiation of the dynamic algorithm and the scheme of handling the history data and the predicted values in differentiation, which is crucial in computing correct derivatives, are described. Besides, we show how to avoid Newton loops in the DSA algorithm, when such a loop is present in the constitutive algorithm. Numerical examples show that, despite a great complexity of the solution algorithm for the finite-rotation elastic-plastic shells, it is feasible to compute analytical design derivatives of very good accuracy. Keywords:Explicit dynamics, Finite rotation shell, Elastic-plastic material, Analytical Design Sensitivity Analysis for constitutive parameters Affiliations:
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9. | Wiśniewski K., Turska E., Enhanced Allman quadrilateral for finite drilling rotations, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 0045-7825, DOI: 10.1016/j.cma.2005.11.003, Vol.195, pp.6086-6109, 2006 Abstract: The paper concerns a four-node quadrilateral element based on Allman shape functions undergoing finite (unrestricted) drilling rotations, and aims at improving its accuracy and facilitating its implementation. New Allman shape functions for finite drilling rotations, Enhanced Assumed Displacement Gradient method for formulations with rotations, Enhanced Allman finite elements Affiliations:
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10. | Wiśniewski K., Kowalczyk P., Turska E., On the computation of design derivatives for Huber–Mises plasticity with non‐linear hardening, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.678, Vol.57, No.2, pp.271-300, 2003 Abstract: This paper concerns design sensitivity analysis (DSA) for an elasto–plastic material, with material parameters depending on, or serving as, design variables. The considered constitutive model is Huber–Mises deviatoric plasticity with non‐linear isotropic/kinematic hardening, one which is applicable to metals. design sensitivity analysis, elasto–plastic material with non‐linear hardening, parallel finite element code Affiliations:
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11. | Sokołowski M., Turska-Kłębek E., On the Approximate Evaluation of Interaction of Cracks in Elastic Media, Rozprawy Inżynierskie, ISSN: 0867-888X, Vol.31, No.1, pp.115-150, 1983 Abstract: A method of approximate analysis is presented concerning the state of stress, and the stress intensity factors in particular, in elastic media subject to a plane state of strain and containing arbitrary arrays of cracks. In the case when ·the crack distribution is not too dense, the method proposed makes possible the determination of the required stress parameters in a manner resembling that used in solving the statically indeterminate systems of structural mechanics. Affiliations:
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12. | Turska E., Stacjonarny ruch szczeliny w polu sił skupionych, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.21, pp.1-36, 1981 |
List of chapters in recent monographs
1. 637 | Wiśniewski K., Turska E.♦, Analysis of Shells, Plates, and Beams: A State of the Art Report, rozdział: On Transverse Shear Strains Treatment in Nine-Node Shell Element MITC9i, Springer, pp.421-440, 2020 | |
2. 613 | Wiśniewski K., Turska E.♦, Recent Developments in the Theory of Shells, rozdział: On Performance of Nine-Node Quadrilateral Shell Elements 9-EAS11 and MITC9i, Springer, pp.711-725, 2019 | |
3. 507 | Wiśniewski K., Turska E.♦, Shell-like Structures. Advanced Theories and Applications, rozdział: Selected topics on mixed/enhanced four-node shell elements with drilling rotation, Springer International Publishing, 572, pp.247-288, 2017 | |
4. 51 | Wiśniewski K., Turska E.♦, Shell-like Structures. Non-classical Theories and Applications, rozdział: Recent Improvements in Hu-Washizu Shell Elements with Drilling Rotations, Springer, pp.391-412, 2011 |
Conference abstracts
1. | Wiśniewski K., Turska E.♦, Recent improvements to nine-node shell element MITC9 with drilling rotations, SSTA 2017, Shell Structures: Theory and Applications, 2017-10-11/10-13, Gdańsk (PL), Vol.4, pp.399-402, 2018 Abstract: The paper describes our improved 9-node quadrilateral shell element MITC9i, which is derived for the Reissner-Mindlin shell kinematics, the extended potential energy functional and Green strain. 1. The MITCi technique is used to avoid locking and it is based on the improved transformations proposed in (Wisniewski & Panasz 2013) for a membrane element. Here, these transformations are extended to bending/twisting and transverse shear shell strains. 2. To reduce the shape distortion effects, the so-called corrected shape functions (CSF) of (Celia & Gray 1984) are used instead of the isoparametric ones, and we propose the method of computation the shift parameters for non-flat shell elements. 3. The drilling rotations are included via the drilling Rotation Constraint and the penalty method. This rotation is used in the multiplicative/additive update scheme valid for large (unrestricted) rotations. The effect of the MITC9i technique and the CSF is that all three patch tests are passed, also for shifted side nodes along the straight edges and for arbitrary shifts of an interior node. The MITC9i shell element was subjected to a range of linear and non-linear numerical tests described in (Wisniewski & Turska 2017); here we provide additional examples illustrating its accurate and robust behavior. Keywords:9-node shell element MITC9,two-level approximation of strains, corrected shape functions, node shift parameters, drilling rotations Affiliations:
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2. | Wiśniewski K., Turska E.♦, Recent results on nine-node shell elements using two-level approximation of strain, SolMech 2016, 40th Solid Mechanics Conference, 2016-08-29/09-02, Warszawa (PL), No.P122, pp.1-2, 2016 Keywords: finite element method, shell elements Affiliations:
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3. | Wiśniewski K., Turska E.♦, Recent improvements in mixed/enhanced shell elements with drilling rotation, SolMech 2014, 39th Solid Mechanics Conference, 2014-09-01/09-05, Zakopane (PL), pp.27-28, 2014 | ||||||||||
4. | Wiśniewski K., Turska E.♦, On mixed/enhanced Hu-Washizu shell elements with drilling rotation, SSTA, 10th Jubilee Conference on Shell Structures - Theory and Applications, 2013-10-16/10-18, Gdańsk (PL), DOI: 10.1201/b15684-117, Vol.3, pp.469-472, 2014 Abstract: Mixed/enhanced four-node shell elements with six dofs/node based on the Hu-Washizu (HW) functional are developed for Green strain. The shell HW functional is derived from the shell potential energy functional instead of from the three-dimensional HW functional. Partial HW functionals, differing in the bending/twisting part and the transverse shear part, are obtained. For the membrane part of HW shell elements, a 7-parameter stress, a 9-parameter strain and a 2-parameter EADG enhancement are selected as performing best. The assumed representations of stress and strain are defined in skew coordinates in the natural basis at the element's center. The drilling rotation is included through the drilling Rotation Constraint (RC) equation and the Perturbed Lagrange method. The spurious mode is stabilized using the gamma method. Several versions of shell HW elements are tested using several benchmark examples and the optimally performing element is selected (HW29) in (Wisniewski & Turska 2012). Affiliations:
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5. | Wiśniewski K., Turska E.♦, On Shell Elements Derived from Hu-Washizu Functional, SolMech 2012, 38th Solid Mechanics Conference, 2012-08-27/08-31, Warszawa (PL), pp.228-229, 2012 | ||||||||||
6. | Wiśniewski K., Kowalczyk P., Turska E., DSA for Elastic-plastic Shells and Explicit Dynamics, 8th U.S. National Congress on Computational Mechanics, 2005-07-24/07-28, Austin, Texas (US), No.1681, pp.1, 2005 Keywords: design sensitivity analysis, finite element method, shell structures, elasto-plasticity Affiliations:
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7. | Wiśniewski K., Kowalczyk P., Turska E., DSA for elastic-plastic finite rotation shells under dynamic loads, ICTAM XXI, 21st International Congress of Theoretical and Applied Mechanics, 2004-08-15/08-21, Warszawa (PL), No.12679, pp.361, 2004 Keywords: Design sensitivity analysis, finite element method, finite rotations, shell elements Affiliations:
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8. | Wiśniewski K., Kowalczyk P., Turska E., DSA for elastic-plastic finite rotation shells under dynamic loads, ICTAM04, 21st International Congress of Theoretical and Applied Mechanics, 2004-08-15/08-21, Warszawa (PL), No.12679, pp.1-2, 2004 Abstract: The paper describes a constitutive algorithm for elastic-plastic finite rotation shells and explicit dynamics with design derivatives calculated w.r.t. We show that despite a great complexity of the solution algorithm for the finite-rotation elastic-plastic shells, it is feasible to compute analytical design derivative of this algorithm, and the yielded sensitivities are of very good accuracy. Keywords:design sensitivity analysis, finite elment method, shell structures, dynamics, finite rotations Affiliations:
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