A three-dimensional finite element method with arbitrary polyhedral elements

The ‘variable-element-topology finite element method’ (VETFEM) is a finite-element-like Galerkin approximation method in which the elements may take arbitrary polyhedral form. A complete development of the VETFEM is given here for both two and three dimensions. A kinematic enhancement of the displacement-based formulation is also given, which effectively treats the case of near-incompressibility. Convergence of the method is discussed and then illustrated by way of a 2D problem in elastostatics. Also, the VETFEM’s performance is compared to that of the conventional FEM with eight-node hex elements in a 3D finite-deformation elastic–plastic problem. The main attraction of the new method is its freedom from the strict rules of construction of conventional finite element meshes, making automatic mesh generation on complex domains a significantly simpler matter