Abstract
A class of boundary-value problems of the dynamic theory of elasticity, which has not been studied to any great extent, is investigated. In these problems all the components of the displacement vector and the stress vector are specified on part of the boundary of the body (nothing is known about the components of these fields on the remaining part of the boundary). A uniqueness theorem is proved. The problem is investigated by reducing the boundary-value problem to a system of Fredholm integral equations of the first kind with smooth kernels. A scheme for the numerical determination of the unknown fields is proposed, based on a combination of the boundary-element method and the Tikhonov regularization method. A number of model examples in establishing the wave fields for an anisotropic body are considered.
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