A Personal Computer Aided Finite Element Method for Inverse Analysis. An Identification Method of Unknown Boundary Condition by Influence Function Method.

Abstract

This paper presents a new inverse analysis method using an influence function method in a finite element method (FEM) on a small memory capacity machine such as a microcomputer and a personal computer. First, we discuss the problems of the inverse analysis using the FEM. Especially, the size of unknown vectors is larger than that of known ones in the FEM equation including unknown boundary condition. This FEM is usually unsolvable. Second, an inverse compliance matrix is introduced into the FEM. Then, we formulate a solvable FEM for inverse problems like unknown boundary condition. Although a compliance matrix is obtained using the influence function method in the ordinary FEM on the small machine, the compliance matrix must be divided into smaller submatrices for the small machine. We calculate the inverse compliance submatrices. From the above procedures, we establish a FEM for inverse analysis on the small machine. Finally, it is verified that this FEM for inverse analysis is exact from the numerical solution of a three-dimensional elastic finite element model on the small machine.