Boundary integral equations for coupled structures in solid mechanics — the direct method

Abstract

The coupled structures consist of two- or three-dimensional bounded or unbounded domains of different anisotropic materials. The domains are non-smooth in general, edges and corners can appear. There are different boundary conditions on the exterior boundary and standard coupling conditions on the interfaces. The so called “direct method” is used for the derivation of appropriate boundary integral equations, which is based on a system of boundary integral equations given by the Cal-deron projector.

This leads to “local” pseudo-differential operator equations with corresponding STEKLOV-POINCARÉ operators on the interface.

Existence, uniqueness and regularity of the solutions are discussed.

Keywords:

• calderon projectors
• boundary integral equations
• sovability
• regularity