Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomogeneous material properties

This paper presents the local boundary integral formulation for an elastic body with nonhomogeneous material properties. All nodal points are surround ed by a simple surface centered at the collocation point. Only one nodal po int is included in each the sub-domain. On the surface of the sub-domain, b oth displacements and traction vectors are unknown generally. If a modified fundamental solution, for governing equation, which vanishes on the local boundary is chosen, the traction value is eliminated from the local boundar y integral equations for all interior points. For every sub-domain, the mat erial constants correspond to those at the collocation point at the center of sub-domain. Meshless and polynomial element approximations of displaceme nts on the local boundaries are considered in the numerical analysis.