An efficient algorithm for finite-difference modeling of mixed-boundary-value elastic problems

The paper describes an efficient numerical scheme for the solution of displacements and stresses in mixed-boundary-value elastic problems of solid mechanics. A new variable reduction scheme is used to develop the computational model. Solution of both two- and three-dimensional problems of linear elasticity is considered in the present paper. In the present approach, the problems are formulated in terms of a potential function, defined in terms of the displacement components. Compared to the conventional computational approaches, the present scheme is capable of providing numerical solution of higher accuracy with less computational effort. Application of the present finite-difference modeling scheme is demonstrated through the solutions of a number of practical stress problems of interest, and the results are compared with those obtained by the standard method of solution. The comparison of the results establishes the rationality as well as suitability of the present variable reduction scheme.