The new paradigm of finite element solutions with overlapping elements in CAD – Computational efficiency of the procedure

Abstract

We consider the new paradigm of finite element analysis, present an effective overlapping finite element, and study the computational efficiency of the discretization scheme.The important new ingredient in the formulation of the overlapping element is that, unlike in meshless methods, we only use local polynomial functions in the displacement interpolations. We achieve this property by replacing the Shepard functions by local polynomials. As a consequence, the bandwidth of the resulting stiffness matrix for the overlapping finite element is much reduced when compared with earlier developments.We study the distortion insensitivity of the new overlapping finite element, the convergence properties and the required computational effort when compared with the use of the traditional 4-node finite element and that element with covers. The results show the overlapping element to be very promising, in particular in the new paradigm of analysis using finite elements in CAD.