Hybrid-Trefftz stress elements for three-dimensional elastoplasticity

  • Flávio L.S. Bussamra Instituto de Pesquisas Tecnológicas do Estado de São Paulo
  • Paulo de Mattos Pimenta Escola Politécnica da Universidade de São Paulo
  • João A. Teixeira de Freitas Universidade Técnica de Lisboa

Abstract

The stress model of the hybrid-Trefftz finite element formulation is applied to the elastoplastic analysis of solids. The stresses and the plastic multipliers in the domain of the element and the displacements on its boundary are approximated. Harmonic and orthogonal hierarchical polynomials are used to approximate the stresses, constrained to solve locally the Beltrami governing differential equation. They are derived from the associated Papkovitch-Neuber elastic displacement solution. The plastic multipliers are approximated by Dirac functions defined at Gauss points. The finite element equations are derived directly from the structural conditions of equilibrium, compatibility and elastoplasticity. The non-linear governing system is solved by the Newton method. The resulting Hessian matrices are symmetric and highly sparse. All the intervening arrays are defined by boundary integral expressions or by direct collocation. Numerical applications are presented to illustrate the performance of the model.

Keywords

References

[1] ABAQUS Standard, Version 5. 7. Hibbit, Karlsson & Sorensen, Inc., 1997.
[2] J.P.M. Almeida. Janela: Uma Interface Gráfica Destinada a aplicações de Mecânica Computacional, versão preliminar. Instituto Superior Técnico, 1992.
[3] C.A. Brebbia, J.C.F. Telles, J.C.F., L.C. Wróbel. Boundary Element Techniques, Springer-Verlag, Berlin, 1984.
[4] F.L.S. Bussamra. Hybrid-Trefftz Finite Elements: an Elastoplastic Model for Three-Dimensional Solids (in Portuguese). Ph.D. thesis. Escola Politécnica, Universidade de São Paulo, Brazil, 1999.
[5] L.M.S.S. Castro. Wavelets and Walsh Series for the Finite Element Method, (in Portuguese). Ph.D. thesis. Instituto Superior Técnico, Technical University of Lisbon, Portugal, 1996.
Published
Mar 2, 2023
How to Cite
BUSSAMRA, Flávio L.S.; PIMENTA, Paulo de Mattos; TEIXEIRA DE FREITAS, João A.. Hybrid-Trefftz stress elements for three-dimensional elastoplasticity. Computer Assisted Methods in Engineering and Science, [S.l.], v. 8, n. 2-3, p. 235-246, mar. 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1167>. Date accessed: 23 nov. 2024.
Section
Articles