Optimal rigid inclusion shapes in elastic bodies with cracks

被引：0
作者：
A. Khludnev
M. Negri
机构：
[1] Lavrentyev Institute of Hydrodynamics,Russian Academy of Sciences
[2] University of Pavia,Department of Mathematics
来源：
Zeitschrift für angewandte Mathematik und Physik | 2013年 / 64卷
关键词：
Primary 74R10; Secondary 49J40; Crack; Rigid inclusion; Inclusion shape; Mutual non-penetration; Variational inequality; Control problem;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The paper concerns the control of rigid inclusion shapes in elastic bodies with cracks. Cracks are located on the boundary of rigid inclusions and in the bulk. Inequality type boundary conditions are imposed at the crack faces to guarantee mutual non-penetration. Inclusion shapes are considered as control functions. First we provide the problem formulation and analyze the shape sensitivity with respect to geometrical perturbations of the inclusion. Then, based on Griffith criterion, we introduce the cost functional, which measures the shape sensitivity of the problem with respect to the geometry of the inclusion, provided by the energy release rate. We prove existence of optimal shapes for the problem considered.
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页码：179 / 191
页数：12
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