Performance evaluation of iterative GFVM on coarse unstructured triangular meshes and comparison with matrix manipulation based solution methods

A matrix free unstructured Galerkin Finite Volume Method (GFVM) is adopted for solving plane-stress two dimensional Cauchy equilibrium equations. The algorithm is developed based on the Galerkin method, for the solution of structural problems on unstructured linear triangular element meshes. The developed shape function free Galerkin Finite Volume solver computes stresses and displacements of solid mechanic problems via some iteration. The performance of the introduced algorithm on coarse unstructured meshes is assessed by comparison with computed results of a plane-stress case (with uniformly distributed load on one of its elliptic boundaries and two straight sliding support boundaries), for which an analytical solution is available. The results of the introduced method are presented in terms of stress and strain contours, and the sensitivity of the GFVM solver to mesh coarseness, as well as to the utilized gradual load imposing parameter (which affects the convergence behavior of the model), is assessed. Furthermore, the accuracy of the present matrix free GFVM is compared to the previous matrix manipulation based solution methods.