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The present work proposes the shear type body force dipole (BFD) in addition to the normal type to simulate residual stress fields more properly. Expressions for the displacements and stresses induced by the BFD are derived and formulated in the boundary integral equations which govern the elastic field. In the first step of the numerical approach, the sensitivity matrix is constructed to correlate the BFD distributions with the boundary stresses, and is transformed into the generalized inverse matrix by the singular value decomposition technique. Then the generalized inverse matrix is operated on the boundary stresses so that the unknown BFD distributions are evaluated. Based on the study for the effect of the shear type BFD on stress and displacement, discussions are focused to the accuracy of the inverse analysis and the influencing factors such as the number of stress data. The use of the boundary displacement besides the stress data is not important to improve the accuracy in the present problem. It is also suggested that the accuracy of the evaluated BFD distribution can be improved by the following iteration of forward stress analysis so as to minimize the stress error norm at the boundary.

A study on the inverse analysis of body force dipole (A proposal of shear type body force dipole for more accurate description of residual stress)