A Personal Computer Aided Finite Element Method of Inverse Analysis for Searching and Identification of Unknown Boundary Condition.

Abstract

This paper presents an inverse analysis method for the searching and the identification of unknown boundary condition in a finite element method (FEM) on a small memory capacity machine such as a personal computer. This method is formulated by extending an influence function method. Following two calculation processes are adopted in the method: (1) an alternative calculation process which searches the unknown condition and obtains a relative nodal load distribution, and (2) a calculation process which determines a nodal load ratio of the distribution in (1). Both the distribution and the ratio are obtained through a same stiffness matrix in the FEM equation. Then, the paper also describes an efficient calculation method in the determination of both the distribution and the ratio using the answer of the extention of the influence one. Therefore, the extention of the influence one makes it possible to execute the efficient calculation of the inverse analysis for the identification of unknown boundary condition. Finally, the validity of the inverse analysis method is comfirmed from the numerical solution of a three-dimensional inverse finite element model, as an example of an elastic structure with reinforced members under tension, carried out on a small memory capacity machine.