The purpose of this paper is to show a highly accurate inverse analysis for the problem of lozenge cavity with sharp comer under in-plane and out-of-plane loadings, which is based on the complex variable method using a conformal mapping technique. A method of inverse analysis for the magnitude and direction of initial stresses is represented by use of the exact solutions. The results of inverse analysis are in agreement with the analytic results on high accuracy.
It is important to estimate the stress and displacement around the boundary of cavities or inclusions that exists in machines and structures. Recently, the investigations called the inverse analysis using techniques such as boundary element method(BEM) and finite element method(FEM) have been carried out. The numeric-analytic techniques that estimate the various physical properties for the defects on high accuracy have been developed. In the inverse analysis, the direct analysis is carried out by the assumption of the parameter to be identified first of all. Next, the parameter is repeatedly corrected so that both of analytic value and measuring value may approximate sufficiently. There is a case in which the uniqueness is not always given obtained solution in the time, and inverse analysis is more difficult than direct analysis. And, the discrete techniques contained BEM and FEM are general as analytic techniques. However, there are restrictions in the point of capacities and calculation times and accuracy of the computer. For this, authors have investigated that apply exact elastic solution obtained by theory of complex functions using mapping function to cavity, rigid and elastic inclusion of various shapes (Shozu et al., 1995a, 1995b, 1996). In this study, the main values around the boundary of various lozenge cavities are used as an assistant input information,
