A Trefftz simplified method for the computation of elastic structures

C. Hochard; P. Ladevèze; L. Proslier

C. Hochard CNRS, Universite Paris VI
P. Ladevèze CNRS, Universite Paris VI
L. Proslier CNRS, Universite Paris VI

Abstract

This paper presents a method for a quick evaluation of stresses and displacements for elastostatic problems. A set of polynomial Trefftz functions and a variational formulation are introduced for solving elastostatic problems for simple star-shaped domains. It is shown, through examples, that this approximation allows the computation of the interior large wavelength effects. By a procedure for coupling separate domains, this method is extended to more complex structures, which is a natural extension of the above variational formulation . A discretization of the structure into large substructures, an easy to use and quick computation of the interior solution justify that this method can be termed "simplified". Comparisons with other similar methods are also shown.

Keywords

References

[1] I. Babuska, A. Miller. The post-processing approach in the finite element method. Part 1: Calculation of displacements, stresses and other high derivatives of displacements. Int. J. Num. Meth. Eng., 20: 1085- 1109, 1984.
[2] C.A. Brebbia, S. Walker, Boundary element technique in Engineering. Newne-Butterworth, London, 1980.
[3] G.E. Christian. Sur une méthode de calcu.l des concentrations de contraintes. These de doctorat, Universite Paris VI, Paris, 1993.
[4] G. Duvaut, J .L. Lions. Les inéquations en mécanique et en physique. Dunod, Paris, 1972.
[5] H. Gourgeon, I. Herrera. Boundary methods. C-complete systems for the biharmonic equation. In: C.A. Brebbia, ed., Boundary Element methods, 431- 441. Springer- Verlag, 1981.