弾性体に対する逆問題 : 非等方弾性体,とくに残留応力の入った弾性体の境界値逆問題を中心に(<特集>逆問題)

概要

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Elasticity with residual stress is a special class of anisotropic elasticity. We consider the inverse boundary value problem for this elasticity, that is, the problem of determining the residual stress and the Lame parameters of an elasitic body by measuring the displacements and the tractions at the boundary. Mathematically, these measurements made at the boundary are encoded in the so-called Dirichlet to Neumann map. We develop Stroh's formalism for this elasticity and give the formula of the surface impedance tensor, which is a principal part of the Dirichlet to Neunann map. Then we prove that all the components of residual stress and Lame parameters at the boundary can be identified from the Dirichlet to Neumann map. The derivatives of residual stress at the boundary can also be identified. Finally, by a layer stripping algorithm, we give an approximation for residual stress in the interior from measurements at the boundary.
2000-06-15