2-D boundary value problems of thermoelasticity in a multi-wedge - multi-layered region. Part 1. Sweep method

Abstract

A method proposed earlier to solve the BVP for Poisson's equation in a domain consisting of wedges and plane layers, is discussed and applied to 2D thermoelasticity problems. Linear conditions of general form are prescribed along the exterior boundaries as well as at all the interfaces. The essence of the method consists in combining the Fourier and Mellin transforms along the common interface. This allows to reduce the boundary value problems to special systems of singular equations. The analysis is significantly simplified by incorporating the fact that layers and wedges represent chain-like systems. In the paper, relations between the Fourier (Mellin) transformations of solutions for the layered (wedge-shaped) part of the domain are found by using the sweep method of LINKOV and FILIPPOV (1991, Mecchanica, 26, 195-209). All matrix-functions in the relations are slowly increasing ones. Their asymptotic behaviour is analyzed depending on the types of the exterior boundary conditions.