Analysis of plane elasticity problems using the dual mesh control domain method

Abstract

The dual mesh control domain method (DMCDM) proposed by Reddy combines the advantages of the finite element method (interpolation of variables) and the finite volume method (satisfaction of the global form of the governing equations). Currently, the method has been used to solve two-dimensional heat transfer, fluid and solid mechanics problems on structured meshes of linear right triangular and bilinear rectangular elements. However, such meshes are not useful from the standpoint of most practical problems which are posed on irregular domains. The present study extends the DMCDM for the analysis of plane elasticity problems involving non-rectangular domains meshed with arbitrarily shaped elements. The approach makes use of the isoparametric formulation, in which the primal mesh used for the approximation of the geometry is also used for approximating the dependent unknowns. Several boundary value problems of elasticity are solved using the DMCDM, and the results are compared with those obtained using the finite element method (FEM). The results show that the DMCDM exhibits excellent convergence and accuracy while requiring less computational cost when compared with the FEM.