Complete solutions at or near the boundary nodes of boundary elements for coupled stretching-bending analysis

In boundary element analysis if the field point is located at or near the boundary nodes, its associated integrals may become singular. Although in the literature the displacements and tractions at the boundary nodes have been well solved for the coupled stretching-bending analysis, their related strains and stresses still remain unsolved due to the coincidence of field points and boundary nodes. In this paper to avoid the singular problem, at the boundary nodes the components of stress resultants, bending moments, in-plane strains and plate curvatures in the tangential direction are approximated by finite difference method, whereas the components in normal direction are evaluated with the aid of constitutive laws for the tangential-normal coordinate. After getting the complete solutions at the boundary nodes, the solutions for the points near the boundary are interpolated by the moving least square method. To verify the correctness of the proposed method, examples of the laminated plates with or without holes subjected to in-plane tension, or out-of-plane bending, or transverse loading are illustrated and compared with the solutions obtained by the other methods.