Regularization Algorithm Of Inverse Identification Of Boundary Conditions For Two-dimensional Elasticity Problems By Using The BEM

The basic principles of the boundary element method (BEM) are described in this paper. The applications of the regularization algorithm in the inverse problem of identifying the boundary conditions are further studied. The analytical integral formulas and singular value decomposition are applied to treat 2-D anisotropic potential Cauchy problems of thin body. The nearly singular integrals in the BEM for thin body problems are dealt with by the analytical integral formulas. The system equation is solved by the truncated singular value decomposition technique (TSVD). The undulating-curve method for flux solutions is proposed to select the truncated number associated with useful singular values. The calculated results are in good agreement with the exact solution.The boundary integral equations about the gravity and temperature loading are given in this work. The truncated singular value decomposition technique is applied to treat 2-D inverse elasticity problems. Four sorts of inverse problems are discussed as follows.1 Parts of the boundary conditions are known, the other unknown boundary conditions are determined;2 There is noise in the known boundary conditions, the unknown boundary conditions are calculated;3 Parts of the boundary conditions and the displacement of some internal nodes are known, the unknown boundary conditions are evaluated;4 Parts of the boundary conditions are known in the model in which exists body loading, the unknown boundary conditions are determined.The results of the typical examples illustrate that the calculated results are very consistent with the exact solution.