Field reconstruction in an anisotropic elastic medium

For steady-state vibrations of an anisotropic elastic body of finite dimensions, a method of the determination of the vibration energy flows in the body is proposed. The method is based on the measurements of the surface values of the stress and displacement vectors at a part of the boundary. The proposed algorithm of the wave field reconstruction is reduced to solving nonclassical boundary integral equations of the first kind with smooth kernels. The formulation of these equations does not require the determination of fundamental solutions, but represents a conditionally well-posed problem. The numerical realization of the proposed method is based on the Tikhonov regularization method and the idea of the boundary element method. Numerical experiments consisting in the reconstruction of the displacements and stresses at the boundary of a rectangular and a circular domains of austenitic steel are performed in the framework of a planar problem of the orthothropic elasticity theory.