Boundary mesh free method with distributed sources for 2D elasticity problems

Abstract

This paper presents development Boundary Distributed Source method for 2D elasticity problems, in which sources are located at domain boundary, i.e., without fictitious boundary. Singularities of the kernel are totally removed by replacing the concentrated point sources with area-distributed sources–circular disc centered at the source point in this study–providing new kernels resulting from analytical integration of the original singular fundamental solution and its derivative on the area of the source disc. All the coefficients for Dirichlet and Neumann boundary conditions in the systems of equations can be determined analytically except diagonal coefficients for Neumann boundary conditions; they are calculated indirectly by the consideration of two reference solutions of rigid body motion in the two directions.