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首页> 外文期刊>Journal of applied and industrial mathematics >Optimal Control of the Layer Size in the Problem of Equilibrium of Elastic Bodies with Overlapping Domains
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Optimal Control of the Layer Size in the Problem of Equilibrium of Elastic Bodies with Overlapping Domains

机译：具有重叠域的弹性体平衡问题中的层大小最优控制

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摘要

We consider the problem of equilibrium of a two-layer elastic body. The first of the layers contains a crack,while the second is a circle centered at one of the crack tips. The round layer is glued by its boundary to the first layer. The unique solvability is proved for this problem in the nonlinear formulation. An optimal control problem is also considered. The radius a of the second layer is chosen as a varying parameter under assumption that a takes positive values from a closed interval. It is shown that there are a value of a minimizing the functional that characterizes how potential energy depends on the crack length and a value of a minimizing the functional that characterizes the opening of the crack.
机译：我们考虑两层弹性体的平衡问题。第一层包含裂纹，第二层是以裂纹尖端之一为中心的圆。圆形层通过其边界粘贴到第一层。在非线性公式中证明了该问题的独特可解性。还考虑了最佳控制问题。在假设a从闭合间隔取正值的情况下，选择第二层的半径a作为变化参数。示出了具有最小化表征势能如何取决于裂纹长度的函数的值以及具有最小化表征裂纹的开口的函数的值。

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