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首页> 外文期刊>Structural Optimization: Computer-Aided Optimal Design of Stressed Systems and Components >Exact analytical solutions for non-selfadjoint variable-topology shape optimization problems: Perforated cantilever plates in plane stress subject to displacement constraints .1.
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Exact analytical solutions for non-selfadjoint variable-topology shape optimization problems: Perforated cantilever plates in plane stress subject to displacement constraints .1.

机译：非自伴变拓扑形状优化问题的精确解析解：受位移限制的平面应力中的多孔悬臂板.1。

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Lurie (1994, 1995a, b) proved recently that variable-topology shape optimization of perforated plates in flexure for non-selfadjoint problems leads to rank-2 microstructures which are in general nonorthogonal. An extension of the same optimal microstructures to perforated plates in plane stress will be presented in Part II of this study. Using the above microstructure, the optimal solution is derived in this part for cantilever plates in plane stress, which are subject to two displacement constraints. For low volume fractions the above solutions are shown to converge to the known truss solutions of Birker et al. (1994). The problem of homogenizing the stiffness of nonorthogonal rank-2 microstructures is also discussed.
机译：Lurie（1994，1995a，b）最近证明，针对非自伴问题的挠性多孔板的可变拓扑形状优化导致了通常为非正交的2级微观结构。本研究的第二部分将介绍在平面应力下将相同的最佳微观结构扩展到多孔板的情况。使用上述微观结构，在此部分中，针对受到两个位移约束的平面应力悬臂板，得出了最佳解决方案。对于低体积分数，上述解决方案已显示收敛至Birker等人的已知桁架解决方案。 （1994）。还讨论了使非正交rank-2微观结构的刚度均匀化的问题。

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