Prof. Krzysztof Wiśniewski, Ph.D., Dr. Habil., Eng.

Department of Information and Computational Science (ZIiNO)
Division of Computational Analysis of Advanced Structures (ZeKAZK)
position: professor
telephone: (+48) 22 826 12 81 ext.: 328
room: 410
e-mail: kwisn
personal site: http://bluebox.ippt.pan.pl/~kwisn/

Doctoral thesis
1985Analiza numeryczna statycznej stateczności powłoki cylindrycznej obciążonej wiatrem 
supervisor -- Prof. Henryk Frąckiewicz, Ph.D., Dr. Habil., Eng., IPPT PAN
421 
Habilitation thesis
1998Finite rotations of shells and beams. Extended equations and numerical models 
Professor
2011-07-15Title of professor
Supervision of doctoral theses
1.2008-10-30Panasz Przemysław  Nieliniowe modele powłok z 6 stopniami swobody bazujące na dwustopniowych aproksymacjach617
 
2.2008-06-26Sadłowski Piotr  Parametryzacje rotacji i algorytmy rozwiązywania równań dynamiki z rotacyjnymi stopniami swobody612
 

Recent publications
1.Jarzębski P., Wiśniewski K., Taylor R.L., On parallelization of the loop over elements in FEAP, COMPUTATIONAL MECHANICS, ISSN: 0178-7675, DOI: 10.1007/s00466-015-1156-z, Vol.56, pp.77-86, 2015
Abstract:

In this paper, we consider parallelization of the loop over elements using OpenMP in FEAP (Taylor, 2014), which is a research FE code, very popular at universities. Even for a serial version of FEAP (a cluster version also exists) such a parallelization is a non-trivial task due to the existing architecture of this code, which complicates efficient parallelization. First, we compare the serial version of FEAP to the parallel code Warp3D (Dodds et al., 2014), considering the usage of time and memory. As we found, Warp3D is much faster but uses more memory than FEAP. An analysis of Warp3D helps us to devise our method of parallelization of the loop over elements. Next, we describe several changes in FEAP, which were necessary to parallelize the loop over elements using OpenMP. In particular, the subroutine assembling elemental matrices is identified as crucial to good performance, and several directives for the mutual exclusion synchronization of OpenMP are implemented and tested. Finally, we demonstrate the performance of the parallelized FEAP, designated as ompFEAP, on numerical examples involving 3D and shell elements of FEAP as well as user’s elements. We conclude that ompFEAP, using the directive ATOMIC for synchronization of the assembling, provides a very good speedup and efficiency.

Keywords:

Parallelization, OpenMP, Finite element method, FEAP, 3D and shell elements

Affiliations:
Jarzębski P.-IPPT PAN
Wiśniewski K.-IPPT PAN
Taylor R.L.-University of California, Berkeley (US)
2.Wiśniewski K., Panasz P., Two improvements in formulation of nine-node element MITC9, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.4399, Vol.93, pp.612-634, 2013
Abstract:

The paper concerns a well-known two-dimensional nine-node quadrilateral element MITC9, which is based on two-level approximations of strains (assumed strain method). The element has good accuracy, but does not pass the patch test.

As the first improvement, we propose a modification of the element's transformations, partly resolving the problem with the patch test. The source of the problem is the use of covariant components in a (local) natural co-basis, different at each sampling point.

As the second improvement, we use the corrected shape functions of Celia MA, Gray WG. An improved isoparametric transformation for finite element analysis. International Journal for Numerical Methods in Engineering 1984; 20:1447–1459, extending their applicability to the nine-node element for plane elasticity and the 3 × 3 integration. Originally, they are tested for an eight-node element for the heat conduction equation and the 4 × 4 integration.

The improved element, designated as MITC9i, is based on the Green strain and derived from the potential energy for the plane stress condition. It is subjected to a range of tests, to confirm that it passes the patch test for several types of mesh distortions, to prove its coarse mesh accuracy and the absence of locking as well as to establish its sensitivity to mesh distortions.

The improved element MITC9i performs substantially better than the MITC9 element, QUAD9** element, and our previous 9-AS element.

Keywords:

nine-node element, two-level approximation of strains, assumed strain method, two-dimensional MITC9, patch test, sensitivity to shape distortions, coarse mesh accuracy

Affiliations:
Wiśniewski K.-IPPT PAN
Panasz P.-IPPT PAN
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.

To reduce the deterioration of accuracy when nodes are shifted, we assess the corrected shape functions of Celia and Gray (1984 [10]) as a replacement for the standard isoparametric ones. In Celia and Gray (1984 [10]), the corrected shape functions were tested for an eight-node element, the heat conduction equation and the 4×4 integration. Here, we test their applicability to nine-node elements for plane elasticity and the 3×3-point integration.

We modify and examine four elements: QUAD9⁎⁎ (Huang and Hinton, 1986 [15]), MITC9 [1] and ours 9-AS (Panasz and Wisniewski, 2008 [21]) and MITC9i (Wisniewski and Panasz, 2012 [26]). The elements are subjected to a range of tests involving several types of mesh distortions, to confirm passing of various forms of the patch test, to prove the absence of locking as well as to establish their coarse mesh accuracy and sensitivity to mesh distortions. We show that all the tested elements benefit from using the corrected shape functions, but still remain significant differences in their performance.

Keywords:

Two-dimensional nine-node elements, Corrected shape functions, Two-level approximations of strains, Patch tests, Shape distortions

Affiliations:
Panasz P.-IPPT PAN
Wiśniewski K.-IPPT PAN
Turska E.-Polish-Japanese Academy of Information Technology (PL)
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.

The shell HW functional is derived from the shell potential energy functional, which is an alternative to the derivation from the three-dimensional HW functional. This method is more versatile as it enables the derivation of the so-called partial HW functionals, with different treatment of the bending/twisting part and the transverse shear part of strain energy.
For the membrane part of HW shell elements, a seven-parameter stress, a nine-parameter strain and a two-parameter enhanced assumed displacement gradient enhancement are selected as optimal. The assumed representations of stress and strain are defined in skew coordinates in the natural basis at the element's center. This improves accuracy and has positive theoretical consequences.
The drilling rotation constraint equation is treated by the perturbed Lagrange method. The faulty term resulting from the equal-order approximations of displacements and the drilling rotation is eliminated, and one spurious mode is stabilized using the gamma method. The proposed formulation is insensitive to the element's distortions and yields a large radius of convergence in the examples involving in-plane bending.

The performance of 4 four-node shell HW elements, having different bending/twisting and transverse shear parts, is analyzed on several numerical examples. Such aspects are considered as: accuracy, radius of convergence, required number of iterations of the Newton method or the arc-length method and time of computations. The element with 29 parameters (HW29) is selected as the best performer.

Keywords:

four-node mixed shell element with six DOFs/node, pure or partial Hu–Washizu functionals, drilling rotation, optimal representations, skew coordinates

Affiliations:
Wiśniewski K.-IPPT PAN
Turska E.-Polish-Japanese Academy of Information Technology (PL)
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.

Two mixed HW elements based on the 5-parameter stress are developed; they use either the 7-parameter or 9-parameter strain representation. The stress and strain representations are assumed in terms of skew coordinates, see [10]. The numerical tests involving coarse distorted meshes are used to assess the effects of using the contravariant strain representation.

The tests show that both elements pass the discrete inf-sup test. Accuracy of the element based on the 9-parameter strain, designated as HW14-S and selected as the best in [9], remains unaffected. Accuracy of the element based on the 7-parameter strain is significantly improved.

Keywords:

Four-node finite elements, Hu–Washizu functional, Plane stress, Mixed elements, Skew coordinates, Contravariant assumed strain

Affiliations:
Wiśniewski K.-IPPT PAN
Wagner W.-Karlsruhe Institute of Technology (DE)
Turska E.-Polish-Japanese Academy of Information Technology (PL)
Gruttmann F.-Technical University of Darmstadt (DE)
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.

(1) The representations of stress and strain are assumed in skew coordinates associated with the natural basis at the element’s center, which implies that, for a linear elastic case, the homogenous equilibrium equations and the compatibility condition are satisfied point-wise. For stress, the same 5- and 7-parameter representations as for the Hellinger–Reissner (HR) elements by Wisniewski and Turska [Wisniewski K, Turska E. Improved four-node Hellinger–Reissner elements based on skew coordinates. Int J Numer Methods Eng 2008;76:798–836] are used. For strain, a 9-parameter linear representation is selected.
(2) A mixed element HW14-S using a 5-parameter representation of stresses assumed in skew coordinates is developed from the non-enhanced HW functional. This element is equally accurate as our HR5-S element of Wisniewski and Turska (1998), the HR element by Yuan et al. [Yuan K-Y, Huang Y-S, Pian THH. New strategy for assumed stress for 4-node hybrid stress membrane element. Int J Numer Methods Eng 1993;36:1747–63], and the HW elements by Piltner and Taylor [Piltner R, Taylor RL. A quadrilateral mixed finite element with two enhanced strain modes. Int J Numer Methods Eng 1995;38:1783–808; Piltner R, Taylor RL. A systematic construction of B-bar functions for linear and non-linear mixed-enhanced finite elements for plane elasticity problems. Int J Numer Methods Eng 1999;44:615–39], and Piltner [Piltner R. An implementation of mixed enhanced finite elements with strains assumed in Cartesian and natural element coordinates using sparse View the MathML sourceB¯-matrices. Eng Comput 2000;17(8):933–49]. Compared to these HW elements, our element uses a smaller number of parameters.
(3) A mixed/enhanced element HW18 using a 7-parameter representation of stress is developed from the enhanced HW functional. For the elements based on this stress representation, the strain representation has to be enriched; we use a 2-parameter EADG enhancement. Various combinations of the natural, skew and Cartesian coordinates are tested, and these for which this element performs best are selected.
(4) A specific modification of the FTFFTF product, consisting of the expansion of FF and the selection of meaningful terms in the product, was applied to selected elements. With this modification, the element HW14-S performs better for coarse distorted meshes than the HW elements described in the literature.

The developed elements are based on the Green strain, and are tested for linear and non-linear constitutive laws modified by the zero normal stress condition, because they will be used as a membrane part of a shell element. Several numerical tests show their performance, in particular, their robustness to the element’s shape distortion for coarse meshes.

Keywords:

4-Node finite elements, Plane stress, Incremental Hu–Washizu functional, Mixed elements, Mixed/enhanced elements, Skew coordinates

Affiliations:
Wiśniewski K.-IPPT PAN
Turska E.-Polish-Japanese Academy of Information Technology (PL)
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.

We argue that the skew coordinates, not the natural ones, should be associated with the natural basis at the element's center. If 5- and 7-parameter stress representations are assumed in these coordinates, then, for a linear elastic case, the homogenous equilibrium equations and the stress form of compatibility equation are satisfied point-wise.

Two mixed four-node elements are developed and tested:
1. An assumed stress element (HR5-S) is developed from the non-enhanced HR functional, for a 5-parameter representation of stresses, formally identical as the one used, for example, in Pian and Sumihara [Int. J. Numer. Meth. Engng 1984; 20:1685–1695], but in terms of skew coordinates. This element is very simple and uses a smaller number of parameters, but is equally accurate as the elements by Yuan et al. [Int. J. Numer. Meth. Engng 1993; 36:1747–1763] and by Piltner and Taylor [Int. J. Numer. Meth. Engng 1995; 38:1783–1808].
2. An assumed stress/enhanced strain element (HR9) is developed from the enhanced HR functional, for a 7-parameter representation of stress and a 2-parameter enhanced assumed displacement gradient or enhanced assumed strain enhancement. Various forms of 7-parameter representations appearing in the literature are reviewed, and we prove that they are linked by a linear onto transformation. The choice of coordinates for the stress and the enhancement turns out to be the crucial factor, and four combinations of coordinates for which the element performs the best are identified.

Both elements are based on the Green strain, and several numerical tests show their good accuracy, in particular, their robustness to shape distortions for coarse meshes. Two update schemes for the multipliers of modes and the incremental constitutive procedure accounting for the plane stress condition for non-linear materials are tested for large deformation problems.

Keywords:

four-node finite elements, incremental Hellinger–Reissner functional, assumed stress element, assumed stress/enhanced strain element, skew coordinates

Affiliations:
Wiśniewski K.-IPPT PAN
Turska E.-Polish-Japanese Academy of Information Technology (PL)
8.Panasz P., Wiśniewski K., Nine-node shell elements with 6 dofs/node based on two-level approximations, FINITE ELEMENTS IN ANALYSIS AND DESIGN, ISSN: 0168-874X, DOI: 10.1016/j.finel.2008.05.002, Vol.44, pp.784-796, 2008
Abstract:

The paper concerns 9-node quadrilateral shell elements derived for Reissner's kinematics. They are based on the Green strain and potential energy, and are applicable to large (unrestricted) rotations. The characteristic features of the developed elements are as follows:

1. Drilling rotation is included via the drill rotation constraint (RC) imposed by the penalty method. Hence, the elements have 6 dofs per node, i.e. three displacements and three rotational parameters, including drilling rotation.

2. Transverse shear and membrane locking as well as the in-plane shear over-stiffening are avoided using the two-level approximation applied to the strain (assumed strain method). This method does not affect the drilling RC.

3. A modification of the two-level approximation method is proposed, consisting in treating the sampling and the numerical integration together, which results in six sampling points being replaced by two sampling lines. The two-level approximation is applied to components in the ortho-normal basis at the element center, which differs our element from the MITC family of elements, which uses the covariant strain components.

4. Selective reduced integration (SRI) approach is revised. The total functional is split into several parts, and a suitable integration rule is found for each part, yielding an efficient element which shows very good mesh convergence.

Two 9-node shell elements are developed and subjected to a range of benchmark tests, to establish the sensitivity to mesh distortion, the coarse mesh accuracy, and to confirm the lack of locking. Our results are compared with results obtained by the MITC9 element of ADINA and the S9R5 element of ABAQUS.

Keywords:

Nine-node shell elements, 6 dofs/node, Drilling rotation, Two-level approximation, Assumed strain, Selective reduced integration

Affiliations:
Panasz P.-IPPT PAN
Wiśniewski K.-IPPT PAN
9.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:
Wiśniewski K.-IPPT PAN
Kowalczyk P.-IPPT PAN
Turska E.-Polish-Japanese Academy of Information Technology (PL)
10.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.

Firstly, the classical Allman shape functions are valid only for small in-plane rotations, and must be used with a co-rotational frame, which embeds finite rotations. We derive a new form of Allman shape functions, which is valid for finite drilling rotations, and allows to avoid the use of such a frame.

Secondly, the classical Allman quadrilateral shows locking in the in-plane shear test. We study this problem, identify its source, and remove it by enhancing the element with two additional modes, via the Enhanced Assumed Displacement Gradient (EADG) method. To accomplish this, we extend the original version of the method to mixed functionals including rotations.

Two variational formulations including the drilling rotation via the rotation constraint (RC) equation are considered; one based on the Green strain, and the other on the relaxed non-symmetric right stretch strain. Numerical tests of the corresponding finite elements show that the improved Allman elements are as exact in linear tests as the EADG4 element, and perform very well in a severe in-plane shear test for one layer of elements undergoing large rotations.

Keywords:

New Allman shape functions for finite drilling rotations, Enhanced Assumed Displacement Gradient method for formulations with rotations, Enhanced Allman finite elements

Affiliations:
Wiśniewski K.-IPPT PAN
Turska E.-Polish-Japanese Academy of Information Technology (PL)
11.Wiśniewski K., Finite Rotations of Shells and Beams Extended Equations and Numerical Models (Praca habilitacyjna), Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.9, pp.1-178, 1997
12.Wiśniewski K., Holnicki-Szulc J., Rozwiązania konstrukcyjne i sterowanie pracą cieplarni słonecznej, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.40, pp.1-74, 1987
13.Wiśniewski K., Analiza numeryczna statycznej stateczności powłoki cylindrycznej obciążonej wiatrem (Praca doktorska), Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.50, pp.1-144, 1985
14.Wiśniewski K., Analiza numeryczna powłoki cylindrycznej: statyka dla obciążeń niesymetrycznych i drgania swobodne, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.20, pp.1-43, 1984
15.Wiśniewski K., Analiza numeryczna powłoki cylindrycznej: stateczność początkowa pod obciążeniem wiatrem, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.26, pp.1-34, 1984

List of recent monographs
1.
1
Wiśniewski K., Finite rotation shells: Basic equations and finite elements for Reissner kinematics, Lecture Notes on Numerical Methods in Engineering and Sciences, Springer Verlag, pp.1-498, 2010
List of chapters in recent monographs
1.
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
2.
472
Jarzębski P., Wiśniewski K., Advances in Mechanics: Theoretical, Computational and Interdisciplinary Issues, rozdział: Performance of the parallel FEAP in calculations of effective material properties using RVE, CRC Press/Balkema, Taylor & Francis Group, M. Kleiber et al. (Eds.), pp.241-244, 2016
3.
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 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:
Wiśniewski K.-IPPT PAN
Turska E.-Polish-Japanese Academy of Information Technology (PL)
2.Jarzębski P., Wiśniewski K., Evaluation of partial factorization for condensation of shell and solid-shell elemental matrices, SolMech 2016, 40th Solid Mechanics Conference, 2016-08-29/09-02, Warszawa (PL), No.P100, pp.1-2, 2016
Keywords:

finite element methods, solid-shell elements

Affiliations:
Jarzębski P.-IPPT PAN
Wiśniewski K.-IPPT PAN
3.Jarzębski P., Wiśniewski K., On calculation of effective material properties using RVE method by parallelized FE code for shell applications, PCM-CMM 2015, 3rd Polish Congress of Mechanics and 21st Computer Methods in Mechanics, 2015-09-08/09-11, Gdańsk (PL), pp.375-376, 2015
Abstract:

This paper concerns parallelization of an FE code for machines with shared memory in order to speed up computations of large models. We parallelized the loop over elements in the research code FEAP using OpenMP, which required several modifications of the code and a specific method of synchronization for assembling, for details see [2]. The parallel solver was also applied. We demonstrate performance of the parallelized FEAP, designated as ’ompFEAP’, in calculations of effective properties of materials using the RVE method. Two RVE examples are computed, for a heterogenous metal-ceramic composite and for a ceramic foam with a complicated micro-structure. We conclude that ompFEAP provides a very good speedup and efficiency causing only a small increase in memory usage.

Keywords:

parallelization, OpenMP, finite element method, FEAP, RVE, shells

Affiliations:
Jarzębski P.-IPPT PAN
Wiśniewski K.-IPPT PAN
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:
Wiśniewski K.-IPPT PAN
Turska E.-Polish-Japanese Academy of Information Technology (PL)
5.Jarzębski P., Wiśniewski K., Corrected shape functions for six-node triangular element for heat conduction, CMM 2013, 20th International Conference on Computer Methods in Mechanics, 2013-08-27/08-31, Poznań (PL), pp.345-353, 2014
Abstract:

In this paper, we derived the corrected shape functions for 6-node triangular element using the concept proposed in (Celia & Gray 1984). These shape functions were implemented in the two-dimensional 6-node triangular element for heat conduction as a replacement of the isoparametric ones. The numerical tests indicate that, for distorted meshes, the new element is more accurate than the standard element. Comparisons of the accuracy of a range of triangular and quadrilateral elements also are provided.

Keywords:

Six-node triangular element, heat conduction, corrected shape functions, sensitivity to mesh distortion, patch test

Affiliations:
Jarzębski P.-IPPT PAN
Wiśniewski K.-IPPT PAN
6.Jarzębski P., Wiśniewski K., On parallelization of the loop over elements for composite shell computations, SolMech 2014, 39th Solid Mechanics Conference, 2014-09-01/09-05, Zakopane (PL), pp.227-228, 2014
7.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
8.Jarzębski P., Wiśniewski K., On corrected shape functions for six-node triangular elements applied to heat conduction problems, CMM 2013, 20th International Conference on Computer Methods in Mechanics, 2013-08-27/08-31, Poznań (PL), No.MS09, pp.11-12, 2013
9.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
10.Panasz P., Wiśniewski K., Modeling of intersections using the nine-node assumed strain shell element, CMM 2011, 19th International Conference on Computer Methods in Mechanics, 2011-05-09/05-12, Warszawa (PL), pp.162-1-2, 2011
11.Panasz P., Wiśniewski K., On computation of sensitivities of multi-layer shells using elements with additional parameters, CMM 2011, 19th International Conference on Computer Methods in Mechanics, 2011-05-09/05-12, Warszawa (PL), pp.275-1-2, 2011
12.Panasz P., Wiśniewski K., On behavior of nonlinear nine-node shell elements in thin limit, SolMech 2010, 37th Solid Mechanics Conference, 2010-09-06/09-10, Warszawa (PL), pp.320-321, 2010
13.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:
Wiśniewski K.-IPPT PAN
Kowalczyk P.-IPPT PAN
Turska E.-Polish-Japanese Academy of Information Technology (PL)
14.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:
Wiśniewski K.-IPPT PAN
Kowalczyk P.-IPPT PAN
Turska E.-Polish-Japanese Academy of Information Technology (PL)
15.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:
Wiśniewski K.-IPPT PAN
Kowalczyk P.-IPPT PAN
Turska E.-Polish-Japanese Academy of Information Technology (PL)