Detecting stress fields in an optimal structure Part I: Two-dimensional case and analyzer
Detecting stress fields in an optimal structure Part I: Two-dimensional case and analyzer
复制标题
检测最佳结构中的应力场第一部分：二维案例和分析器
DOI：
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发表时间：
2004
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通讯作者：
I. Kucuk
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文献类型：
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作者：
A. Cherkaev;I. Kucuk
本文以二维两相弹性复合材料为研究对象，利用最优性的必要条件研究了最优弹性结构中的应力场。必要条件表明，最佳设计的特征在于三个区域：纯弱材料1的区域1;纯强材料2的区域2;以及材料1和材料2混合以形成最佳微观结构的区域3。为了表征这些区域，我们引入了两个旋转不变的规范N1和N2的应力张量。导出的最优性条件表明不等式N1（σ）<constant 1在区域1成立;不等式N2（σ）> constant 2在区域2成立;两个等式在区域3同时成立：N1（σ）= constant 1，在材料1中; N2（σ）= constant 2，在材料2中。使用这个结果，我们分析次优的项目，并找到如何接近的领域是最优的区域。
In this paper, we investigate the stress fields in optimal elastic structures by the necessary conditions of optimality, studying two-phase elastic composites in two dimensions. The necessary conditions show that an optimal design is characterized by three zones: Zone 1 of pure weak Material 1; Zone 2 of pure strong Material 2; and Zone 3, where Material 1 and Material 2 mix to form an optimal microstructure. To characterize these zones, we introduce two rotationally invariant norms N1 and N2 of a stress tensor. The derived optimality conditions state that the inequality N1(σ)< constant1 holds in Zone 1; the inequality N2(σ)> constant2 holds in Zone 2; and two equalities hold simultaneously in Zone 3: N1(σ)= constant1, in Material 1; N2(σ)= constant2 in Material 2. Using this result, we analyze suboptimal projects and find how close the fields are to the regions of optimality.