A finite difference solution of a steel plate with an internal hole using the displacement potential approach

Abstract

The finite difference technique based on a displacement potential formulation is extended to solve an elastic plane stress problem with geometric perturbations such as holes, arbitrary defects, notches, etc. An elastic steel plate having an internal hole is constrained at one edge and a shear load is applied to the opposite edge. The present problem is solved by using the extended finite difference technique based on displacement potential approach. The different displacement and stress components at different sections of the plate are shown graphically and discussed; from the analysis of stress and displacement components at different sections of the plate, critical regions of the plate are identified. The superiority of the finite difference method (FDM) based on the displacement potential formulation over the finite element method (FEM) is verified by the comparison between the solutions of the present problem by the FDM and FEM. From the comparison between the solutions of the FEM and FDM, it is concluded that the present finite difference technique based on the displacement potential formulation is reliable and can be used to solve the structural elements having internal defects.