Semi‐analytical integration of the elastic stiffness matrix of an axisymmetric eight‐noded finite element

Abstract

The finite element method (FEM) is a numerical method for approximate solution of partial differential equations with appropriate boundary conditions. This work describes a methodology for generating the elastic stiffness matrix of an axisymmetric eight-noded finite element with the help of Computer Algebra Systems. The approach is described as "semi analytical" because the formulation mimics the steps taken using Gaussian numerical integration techniques. The semianalytical subroutines developed herein run 50% faster than the conventional Gaussian integration approach. The routines, which are made publically available for download, 1 should help FEM researchers and engineers by providing significant reductions of CPU times when dealing with large finite element models.