On a finite element method with variable element topology

A new finite-element-like approximation method for problems in solid mechan ics. here called the variable-elements-topology finite element method (VETF EM), is presented. The displacement-basis variational basis of the conventi onal finite element method (FEM) is retained in the VETFEM, as is the discr etization of the problem into elements. However, VETFEM elements are not su bject to any of the geometric or topological restrictions of conventional e lements: they may contain any number of nodes in any arrangement. The polyn omial VETFEM shape functions emerge from a constrained minimization process on each element, instead of from an isoparametric transformation from a pa rent element as in the conventional FEM. All the powerful features normally associated with the conventional FEM are exhibited by the new method. In a ddition, because of the absence of geometric and/or topological restriction s on the elements, automatic mesh generation is enormously simplified. For this reason, the VETFEM is thought to be particularly useful for problems i nvolving very complex geometry, adaptive remeshing, or crack extension. (C) 2000 Elsevier Science S.A. All rights reserved.