A Microcomputer-Aided Three-Dimensional Finite Element Method : An Efficient Composition Method for Stiffness Submatrices and a New LDU Decomposition Method

Abstract

The finite element method (FEM) plays an important role in computer-aided engineering (CAE). The FEM and CAE require the use of a large-capacity machine such as a mainframe computer. Requirement for the utilization of microcomputer-aided FEM (MiFEM) and/or engineering (MiCAE) arises in small- and medium-size companies which are not equipped with a large machine. This paper deals with a MiFEM to analyze three-dimensional large-scale Problems, with the utilization of an external storage unit such as the floppy disk. First, we describe an efficient composition method for small-size submatrices divided from a large-size total stiffness matrix. Next, we present a new LDU decomposition method for submatrices. A new MiFEM is developed using both the efficient composition and the LDU decomposition methods. This MiFEM is equivalent to a generalized version of the ordinary FEM, which is dependent on a large machine, because the MiFEM can be executed on every computer. Furthermore, the MiFEM makes it possible to develop a MiCAE.