The finite volume multigrid (FV/MG) method in plane stress elasticity

The Finite Volume (FV) and the Multigrid (MG) methods have been successfully applied to fluid mechanics, dynamics and heat transfer problems. In this paper, these methods are extended to solve plane stress elasticity problems. The proposed method (FV/MG) employs the equilibrium equations containing stress integrals along the elements boundaries. The boundary integrals are computed using a bilinear interpolation formula for the displacements in two different FV formulations: the node- centred and the cell- centred scheme. In addition, a very effective Multigrid method, already developed by the authors for flow problems, is used. The performance and the accuracy of the two FV/MG schemes are numerically investigated and computational results for two 2D-elasticity test problems are presented, and compared to the Finite Element Method. Using the proposed scheme comparable, to the FEM, results were achieved whereas, acceleration by at least 100 times (in a mesh of 48x16) was achieved.