Trefftz functions in FEM, BEM and meshless methods
Abstract
The paper contains three different multi-domain formulations using Trefftz (T -) displacement approximation/ interpolation, namely the hybrid-displacement FEM, reciprocity based FEM (multi-domain BEM) and the Boundary Meshless Method (BMM) for a single and multi-domain (MD) formulation. All three methods can lead to compatible formulation with the isoparametric FEM, when the displacements along the common boundaries are defined by same interpolation function. All three T-formulations enable to define more complicated elements/subdomains (the T-element can be also a multiply connected region) with integration along the element boundaries, only.
References
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[3] V. Cerruti. Ricerche intorno all'equilibrio dei corpi elastici isotropi. Atti della R. Academia dei Lincei, Memoriae della Classe di Scienzc Fiziche, Matematiche e Naturali, 13: 81, 1881- 1882.
[4] A.H.-D. Cheng, D.T. Cheng. Heritage and early history of the boundary element method. Eng. Anal. With Boundary Elements, 29: 268- 302, 2005.
[5] T.A. Cruse. Numerical solutions in three dimensional elastostatics. Int. J. Solids Struct ., 5: 1259- 1274, 1969.
[2] J. Boussinesq. Application des Potentiels a l'Etude l'Equilibre et du Mouvcment des Solides Elnstiqnes. Gautier-Villars, Paris, 1885.
[3] V. Cerruti. Ricerche intorno all'equilibrio dei corpi elastici isotropi. Atti della R. Academia dei Lincei, Memoriae della Classe di Scienzc Fiziche, Matematiche e Naturali, 13: 81, 1881- 1882.
[4] A.H.-D. Cheng, D.T. Cheng. Heritage and early history of the boundary element method. Eng. Anal. With Boundary Elements, 29: 268- 302, 2005.
[5] T.A. Cruse. Numerical solutions in three dimensional elastostatics. Int. J. Solids Struct ., 5: 1259- 1274, 1969.
Published
2022-11-17
Issue
pp. 417- 426
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Kompiš, V., & Štiavnicky, M. (2022). Trefftz functions in FEM, BEM and meshless methods. Computer Assisted Methods in Engineering and Science, 13(3), 417-426. https://cames3.ippt.pan.pl/index.php/cames/article/view/943
