Free Material Optimization with Fundamental Eigenfrequency Constraints
Free Material Optimization with Fundamental Eigenfrequency Constraints
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DOI：
10.1137/080717122
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发表时间：
2009-03
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影响因子：
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通讯作者：
M. Stingl;M. Kočvara;G. Leugering
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文献类型：
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作者：
M. Stingl;M. Kočvara;G. Leugering
本文的目标是制定并解决受最优结构的最小特征频率约束的自由材料优化问题。这个问题作为线性半定规划的自然表述在数值上是难以解决的。作为替代方案，我们提出了一种新方法，该方法基于半定对偶的非线性半定低秩近似。我们介绍一种基于这种方法的算法并分析其收敛特性。文章最后通过数值实验证明了新方法的有效性。
The goal of this paper is to formulate and solve free material optimization problems with constraints on the smallest eigenfrequency of the optimal structure. A natural formulation of this problem as a linear semidefinite program turns out to be numerically intractable. As an alternative, we propose a new approach, which is based on a nonlinear semidefinite low-rank approximation of the semidefinite dual. We introduce an algorithm based on this approach and analyze its convergence properties. The article is concluded by numerical experiments proving the effectiveness of the new approach.