A non-iterative methodology to reconstruct boundary shapes and conditions in isotropic linear elasticity based on the BEM

Abstract

A non-iterative method is proposed to estimate unknown boundary geometry shapes and boundary conditions in 2D and 3D isotropic linear elasticity problems based on the boundary element method (BEM). A virtual domain with a virtual boundary is introduced to the inverse problem. For the boundary geometry shape identification problem, the displacements of the virtual boundary are obtained through the measurement point displacements and the singular value decomposition is applied to solve the ill-posed matrix. The BEM is used to solve the problem with the displacements of the virtual boundary. The unknown boundary geometry shapes can be estimated by searching the internal point isodisplacement curve. For the boundary condition reconstruction problem, the virtual boundary is overlapped with the real boundary. The displacements of the virtual boundary can also be acquired by the measurement point displacements. The unknown boundary tractions can be calculated by the BEM. Finally, the influences with different virtual domains, measurement points, measurement positions and measurement errors on the results are discussed. The results show that the proposed method is an accurate and efficient way to identify boundary geometry shapes and reconstruct boundary conditions.