Identification of the shape of the inclusion in the anisotropic elastic body
Identification of the shape of the inclusion in the anisotropic elastic body
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DOI：
10.1080/00036819908840727
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发表时间：
1999-02
影响因子：
1.1
通讯作者：
Masaru Ikehata;G. Nakamura;Kazumi Tanuma
中科院分区：
文献类型：
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作者：
Masaru Ikehata;G. Nakamura;Kazumi Tanuma
考虑一个占据区域的弹性体，设D表示一个具有紧包含在Ω中的Lipschitz边界的开子集。假设Ω的弹性张量场具有这样的形式，其中Co是齐次各向异性弹性张量场。用∂Ω上的牵引力表示，对应于∂Ω上的位移场f。我们假设(I)是连通的；(Ii)H的所有分量在D中本质有界；(Iii)H在D中∂D的相对邻域内满足跳跃条件。在这一假设下，我们利用无穷多个f证明了D的唯一判定。
Consider an elastic body which occupies a domain Let D denote an open subset with Lipschitz boundary compactly contained in Ω. Suppose the elasticity tensor field of Ω has the form where Co is a homogeneous anisotropic elasticity tensor field. Denote by the traction on ∂Ω corresponding to a displacement field f on ∂Ω. We assume that (i) is connected; (ii) all component of H are just essentially bounded in D; (iii) H satisfies a jump condition in a relative neighbourhood of ∂D in D Under this assumption, we prove the unique determination of D by means of for infinitely many f. The proof is due to making use of a system of integral inequalities, the Runge approximation theorem and singular solutions.