Trefftz polynomials reciprocity based boundary element formulations for elastodynamics

  • F. Konkol University of Zilina
  • V. Kompis University of Zilina

Abstract

In this paper Trefftz polynomials are used for the BEM (Boundary Element Method) based on the reciprocity relations. BEM provides a powerful tool for the calculation of dynamic structural response in the frequency and time domains. Field equations of motion and boundary conditions are cast into boundary integral equations (BIE) , which are discretized only on the boundary [1]. Trefftz polynomials or other non-singular (e.g. harmonic), Trefftz functions [2] (i.e. functions satisfying all governing differential equations but not the boundary conditions) used in the Betti's reciprocity relations lead to corresponding BIE that do not contain any (weak, strong, hyper) singularities. Fundamental solutions are not needed and evaluation of the field variables inside the domain is simpler.

Keywords

References

[l] J. Dominguez. Boundary elements in dynamics. CMP Elselvier, Essex, first edition, 1993.
[2] V. Kompis, L. Jakubovicova., F. Konkol. Non-singular reciprocity based BEM/ FEM formulations. IUTAM/ IACEM/ IABEM Symposium on Advanced Math. and Comput. Mech. Aspects of the Bound. Elem. Meth. , 264 (61) : 264- 269, 1994.
[3] P. J . Hunter, A. J . Pullan. FEM/ BEM NOTES. Web-based Document, http://www.esc.auckland.ac.nz/Academic/Texts/FEM-BEM-notes.html. 1997.
[4] D. Nardini, C. A. Brebbia. Boundary integral formulation of mass matrices for dynamic analysis. In Topics in Boundary Element Resarch, Vol. 2, Springer-Verlag, Berlin and New York, 1985.
[5] Q.-H. Quin. The trefftz finite and boundary element method. WIT Press Southampton, Boston, first edition, 2000.
Published
Jan 18, 2023
How to Cite
KONKOL, F.; KOMPIS, V.. Trefftz polynomials reciprocity based boundary element formulations for elastodynamics. Computer Assisted Methods in Engineering and Science, [S.l.], v. 11, n. 2-3, p. 239-245, jan. 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1037>. Date accessed: 21 nov. 2024.
Section
Articles