An inverse approach to construct residual stresses existing in axisymmetric structures using BEM

Based on the concept of the inherent strain and BEM, an inverse approach has been proposed for constructing residual stresses existing in axisymmetric structures. Taking into consideration of the efficiency of the algorithm and stability of the solution to the inverse problem, the inherent strains are approximately expressed as a series of smooth basis functions in the form of polynomials. With the presence of the initial stresses in the inverse problem, the boundary integral equation involves a domain integral; in order to preserve the advantage of the BEM, corresponding domain integral is transformed into the boundary integral by means of the dual reciprocity boundary element method. Then, the expression of the sensitivity matrix can be obtained and the distribution of residual stresses constructed efficiently. Numerical examples are given to show the applicability of the presented scheme.