Structural optimization using topological and shape sensitivity via a level set method
Structural optimization using topological and shape sensitivity via a level set method
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发表时间：
2005
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通讯作者：
G. Allaire;F. Gournay;F. Jouve;Anca-Maria Toader
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作者：
G. Allaire;F. Gournay;F. Jouve;Anca-Maria Toader
提出了两种结构形状和拓扑优化方法的数值耦合。一方面，基于经典形状导数的水平集方法易于处理随拓扑变化的边界传播。然而，在实践中，它不允许新孔的成核（至少在二维中）。另一方面，气泡或拓扑梯度法被精确设计为在优化过程中引入新的孔。因此，这两种方法的耦合产生了一种有效的算法，可以在给定的拓扑形状类中摆脱局部极小值。这两种方法都依赖于通过伴随分析计算的梯度概念，并且由于它们在固定的欧拉网格上捕获形状，因此CPU成本低。我们的耦合算法的主要优点是使最终的最优设计在很大程度上独立于初始猜测。
A numerical coupling of two recent methods in shape and topology optimization of structures is proposed. On the one hand, the level set method, based on the classical shape derivative, is known to easily handle boundary propagation with topological changes. However, in practice it does not allow for the nucleation of new holes (at least in 2-d). On the other hand, the bubble or topological gradient method is precisely designed for introducing new holes in the optimization process. Therefore, the coupling of these two method yields an efficient algorithm which can escape from local minima in a given topological class of shapes. Both methods relies on a notion of gradient computed through an adjoint analysis, and have a low CPU cost since they capture a shape on a fixed Eulerian mesh. The main advantage of our coupled algorithm is to make the resulting optimal design largely independent of the initial guess.