Greenʹs matrices for the 2-D Lame system in regions of irregular shape

A method is proposed for the construction of Greenʹs matrices for mixed boundary value problems in regions of irregular shape for the displacement formulation of the plane problem in theory of elasticity. The method is based on the boundary integral equation approach where a kernel matrix B satisfies the 2-D homogeneous Lame system inside the region. This leads to a regular boundary integral equation where the compensating load is applied to the boundary. The Greenʹs matrix is consequently expressed in terms of the kernel matrix B, the fundamental solution matrix of the homogeneous Lame system and a kernel matrix of the inverse regular integral operator. To calculate the stress components, the kernel matrices are differentiated under the integral sign. The proposed method appears highly effective in computing both displacements and stresses.