The derivation of special purpose element functions using complex solution representations

  • Reinhard Piltner University of Nebraska-Lincoln

Abstract

For several elasticity problems, solution representations for the displacements and stresses are available. The solution representations are given in terms of "arbitrary" complex valued functions. For any choice of the complex functions, the governing differential equations are automatically satisfied. Complex solution representations are therefore useful for applications of the Trefftz method. For the analysis of local stress concentrations, due to the local geometry of the boundary curve, such solution representations can be very helpful in the construction of appropriate series of Trefftz functions. In this paper, a few examples are given to demonstrate how to construct Trefftz functions for special purpose finite elements, which include the local solution behavior around a stress concentration or stress singularity.

Keywords

elasticity, complex solution representations, stress singularities, Trefftz functions, Trefftz-type finite elements,

References

[1] E. Trefftz. Ein Gegenstuck zum Ritzschen Verfahren. In: 2. Int. Kongr. für Techn. Mech., pages 131- 137, Zurich, 1926.
[2] J.P.B.M. Almeida, O.J.B.A. Pereira. A set of hybrid equilibrium finite element models for the analysis of three-dimensional solids. Int. J. Numer. Meth. Eng., 39: 2789- 2802, 1996.
[3] N.A. Dumont. The hybrid boundary element method: An alliance between mechanical consistency and simplicity. Appl. Mech. Rev., 42(11): 854- 63, 1989.
[4] J.A.T. Freitas, Z.Y. Ji. Hybrid-Trefftz equilibrium model for crack problems. Int. J. Numer. Meth. Eng., 39: 569- 584, 1996.
[5] 1. Herrera. Trefftz method: A general theory. Numerical Methods for Partial Differential Equations, 16(6): 561-580, 2000.
Published
Jan 26, 2023
How to Cite
PILTNER, Reinhard. The derivation of special purpose element functions using complex solution representations. Computer Assisted Methods in Engineering and Science, [S.l.], v. 10, n. 4, p. 597-607, jan. 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1068>. Date accessed: 13 nov. 2024.
Section
Articles