Solution of some problems of linear plane elasticity in doubly-connected regions by the method of boundary integrals

Abstract

A boundary Fourier expansion method is used to solve the system of field equations of plane, linear elasticity in stresses for homogeneous, isotropic media occupying a doubly-connected domain under given pressures on the boundaries. Two cases are considered: A circular domain with elliptical hole and a rectangular domain with a rectangular hole. In each case, the boundary values of the relevant harmonic functions are obtained and the error in satisfying the boundary conditions is given. Comparison is carried out between the present results on the boundary and those obtained by the usual boundary collocation method. The stress function and the displacement are calculated inside the domain