DUAL FORMULATIONS OF THE BOUNDARY-ELEMENTS METHOD - APPLICATION TO ELASTICITY THEORY PROBLEMS FOR INHOMOGENEOUS BODIES

Alternative variational formulations are considered for the boundary-e lements method (BEM) that utilize the formulation of minimization prob lem of boundary functionals and generalized Trefftz functions of linea r elasticity theory /1/. The variational solutions are approximated by using boundary potentials with the desired density: the formulation i n displacements (line) in place of the interpolation considered earlie r of the double layer potential (DLP) density uses interpolation on th e boundary element (BE) of the simple layer potential (SLP) density ac cording to the nodal values of the displacements; the dual formulation is interpolation on the BE of the PLP density according to the nodal values of the stresses. It is best to use the formulation for solving problems of elasticity theory with mixed boundary conditions, contact problems. In particular, the dual formulation turns out to be effectiv e in solving problems for elastic media with discontinuous elasticity coefficients (piecewise-homogeneous); adjoint conditions must be reali zed in the corresponding variational problem for both the displacement vector and for the stress vector on the surface of discontinuity of t he coefficients. The results obtained in /1/ and in this paper are com pared with the results arising from other BEM formulations.