A general mathematical formulation for finite-difference solution of mixed-boundary-value problems of anisotropic materials

This paper presents a general mathematical model, especially suitable for finite-difference analysis of stresses and displacements of the plane elastic problems of solid mechanics. The present formulation covers the problems of anisotropic, orthotropic and isotropic materials, in which the problem is formulated in terms of a single potential function, defined in terms of the displacement components. In addition, the formulation contains a new scheme of reduction of unknowns to be solved for a particular problem. Compared to the conventional computational approaches, the present scheme gets solution of higher accuracy and in extremely shorter time. The application of the present scheme is demonstrated here through a classical problem of solid mechanics, and the results are compared with the available solutions in the literature.