A Microcomputer-aided Three-dimensional Finite Element Method. A Tandem-type Substructuring Method Using LDU Decomposition Method of Stiffness Submatrices.

Abstract

This paper presents a tandem-type substructuring method using a LDU decomposition method of the small-size stiffness submatrices for developing an efficient calculation method of a microcomputer/personal computer-aided finite element method (FEM). This method needs to utilize the disk memory storage unit such as floppy and hard disks in order to store the data of the stiffness submatrices and/or their decomposed ones. Especially, the stiffness submatrices of the storage unit are divided from a substructure stiffness matrix within the limit of the machine memory capacity to be used. The data of the LDU submatrices are placed in the data set of the stiffness submatrices in order to save storage space in the unit. The FEM using the method is applied to an efficient analysis of a three-dimensional elastic block with semi-cylinder notches under tension. Morover, the FEM is available for an analysis of structures of a large-size matrix required for a memory capacity larger than that of the machine itself. This method also contributes to the decrease of memory capacity and central processing unit time in the conventional FEM.