Discrete gradient method in solid mechanics

A discrete method to boundary value problems in solid mechanics is presented. In this method, the unknown variable and its derivative are defined only at nodes. A discrete gradient operator is constructed with the aid of a tensorial identity on the Voronoi diagram. This operator is utilized in a weak form to derive a discrete Galerkin formulation for the boundary value problem. The theoretical underpins of the methodology are discussed, and the details of computational implementation in two-dimensional elasticity, both small strain and finite strain, are provided. Several benchmark tests are presented to demonstrate the accuracy, convergence, and other properties of the method. Copyright (C) 2007 John Wiley & Sons, Ltd.