Integration Scheme for Elastic Deformation and Stresses

Abstract

The integration scheme is proposed in this paper to solve linear deformation and stresses for elastic bodies. The discretized equations are of the finite difference type such that all of the advantages in the use of a finite difference scheme are preserved. In addition, the boundary traction can be easily converted into Dirichlet boundary condition for the displacement equations without recourse to fictitious points. Three examples are illustrated in this study to examine the performances of the integration scheme. In the case of thermal loading, the integration scheme is seen to provide solution with six-place accuracy while the finite element and the boundary element solutions possess only two- to three-place accuracy at essentially the same number of grid points. A similar situation is believed to exist also in the case of pure mechanical loading, although no exact solution is available for comparison. For a square bimaterial under a thermal loading without boundary traction, the integration scheme is found to successfully predict the existence of the interface zone. Due to its simplicity and efficiency, the integration scheme is expected to have good performance for solid mechanical problems, especially when coupled with heat transfer and fluid flow inside and outside the solid.