Inverse analysis related to stress separation in thermoelastic stress analysis

Thermoelastic stress analysis(TSA) is a technique for measuring stresses through temperature changes induced by the thermoelastic effect of elastic bodies. Since the TSA can only provide the sum of the principal stresses, stress separation is required to obtain individual stress components. This paper deals with stress separation of TSA data. The problem is divided into two: (1) an inverse problem to estimate the unknown boundary values from the sum of the principal stresses inside the body, and (2) a direct problem to derive the stress components inside the body on the basis of the estimated boundary values. This two-step method can be applied to a wide range of practical problems if both the inverse and direct problems are solved by FEM or BEM. In this study, the problem is formulated by BEM. It is shown that careful treatment of the inverse problem is essential for attaining an accurate result of the stress separation. The combination of the truncated singular value decomposition and Hansen's L-curve method is found to be effective for the purpose.