Finite Element Analysis of Some Inverse Elasticity Problems

Abstract

This paper is concerned with the solution of some inverse elasticity problems of practical significance to experimental mechanics. More specifically, the boundary tractions and displacements in an elastically deformed two‐dimensional body are calculated using experimentally determined or specified displacements or strains at a finite number of internal points in the body. A brief description of what inverse problems are and why they are important is given. The finite element method is used with regularization techniques to solve the inverse deformation problems of concern here. Some illustrated numerical examples are presented to demonstrate the method. Through these examples, the effect of the error in the internal data and of the number of measurement points and their location is examined and reported. In addition, potential applications for the method are discussed.