A geometrically versatile finite volume formulation for plane elastostatic stress analysis

A finite volume formulation for discretizing and analysing plane elastostatic problems is described. Equilibrium equations which relate the displacements at the centre of a general quadrilateral cell to those in neighbouring cells are developed. After the application of suitable boundary conditions, an iterative method is employed to solve the resulting system of simultaneous equations and produce the displacement field, from which the strain and stress fields are derived subsequently. Stress distributions for a test problem, an elliptic plate pierced by an elliptic hole and loaded on the outer boundary, are determined for meshes of increasing refinement. The distributions are compared with those determined using triangular and quadrilateral finite elements and the analytical solution.