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Application of Multi-Region Trefftz Method to Elasticity

J. Sladek1, V. Sladek1, V. Kompis2, R. Van Keer3
Institute of Construction and Architecture, Slovak Academy of Sciences, 84220 Bratislava, Slovakia.
Faculty of Mech. Engn., University of Zilina, 01026 Zilina, Slovakia.
Dept. Mathematical Analysis, University of Gent, B-9000 Gent, Belgium.

Computer Modeling in Engineering & Sciences 2000, 1(4), 1-8. https://doi.org/10.3970/cmes.2000.001.453

Abstract

This paper presents an application of a direct Trefftz method with domain decomposition to the two-dimensional elasticity problem. Trefftz functions are substituted into Betti's reciprocity theorem to derive the boundary integral equations for each subdomain. The values of displacements and tractions on subdomain interfaces are tailored by continuity and equilibrium conditions, respectively. Since Trefftz functions are regular, much less requirements are put on numerical integration than in the traditional boundary integral method. Then, the method can be utilized to analyse also very narrow domains. Linear elements are used for modelling of the boundary geometry and approximation of boundary quantities. Numerical results for a rectangular plate with varying aspect ratio and cantilever beam are presented.

Keywords

plynomial Trefftz functions, direct formulation, linear approximation, boundary integral equation

Cite This Article

Sladek, J., Sladek, V., Kompis, V., Keer, R. V. (2000). Application of Multi-Region Trefftz Method to Elasticity. CMES-Computer Modeling in Engineering & Sciences, 1(4), 1–8.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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