On restoring of the pre-stressed state in elastic bodies

This research is devoted to the development of theoretical foundations for identification of an essentially inhomogeneous prestressed state by analyzing the gain‐frequency characteristic of boundary points of the body. The proposed scheme to the reconstruction of inhomogeneous prestresses is constructed on the iterative processes. It includes the finite element solution of the direct problem and the regularizing procedure to solve the Fredholm integral equation of the first kind in the inverse problem. In the series of one‐dimensional model examples it was shown that this scheme is effective. This research is devoted to the development of theoretical foundations for identification of an essentially inhomogeneous prestressed state by analyzing the gain‐frequency characteristic of boundary points of the body. The proposed scheme to the reconstruction of inhomogeneous prestresses is constructed on the iterative processes. It includes the finite element solution of the direct problem and the regularizing procedure to solve the Fredholm integral equation of the first kind in the inverse problem. In the series of one‐dimensional model examples it was shown that this scheme is effective.