Some remarks on the applicability of rectangular elements to plane strain boundary value problems

  • Andrzej Jarzębowski Systems Research Institute of the Polish Academy of Sciences
  • Jan Maciejewski Systems Research Institute of the Polish Academy of Sciences

Abstract

The aim of this paper is the discussion on the applicability of some rectangular elements to plane strain boundary value problems. Four different elements were considered: 4-node, 5-node, Serendipity 8-node and Lagrangian 9-node. Two cases: the material layer loaded by a concentrated vertical force and the same layer loaded by a symmetrical rigid punch were discussed. An elastic material was used to avoid the influence of the constitutive model on solutions. To model interface behaviour on the contact surface a Coulomb friction condition was applied. The use of the 4- and 5-node elements resulted in the predictionf the "island" pattern of stress and strain tensors distributions and their non-applicability was proved independently fTom the boundary condition. The 8-node element predicted erroneous distributions of nodal forces and should be avoided in the case of contact problems. Among the discussed group of elements only the 9-node element turned out to be applicable for boundary value problems under plane strain condition.

Keywords

References

[l] A. Jarzębowski and Z. Mróz. A constitutive model for sands and its application to monotonic and cyclic loading. Proc. Constitutive Equations for Gmnular Non-Cohesive Soils, Saada and Bianchini (eds.), Balkema, Rotterdam, 307-323, 1988.
[2] A. Jarzębowski and J. Maciejewski. Compaction of a cohesive soil layer under a rigid roll experiment and numerical prediction. XIX-th ICTAM, Kyoto, Japan, 25-31 August 1996.
[3] E. Hinton and D.R..J. Owen. An Introduction to Finite Element Computations. Pineridge Press Limited, Swansea, 1979.
[4] O.C. Zienkiewicz and R..L. Taylor. The Finite Element Method. 4-th edition, Me Graw-Hill, New Jersey, 1989.
[5] J.T. Oden and J.N. Reddy. An Introduction to the Mathematical Theory of Finite Elements. John Wiley and Sons, New York, 1976.
Published
May 31, 2023
How to Cite
JARZĘBOWSKI, Andrzej; MACIEJEWSKI, Jan. Some remarks on the applicability of rectangular elements to plane strain boundary value problems. Computer Assisted Methods in Engineering and Science, [S.l.], v. 5, n. 3, p. 299-309, may 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1346>. Date accessed: 13 nov. 2024.
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Articles