Stress constrained shape and topology optimization with fixed mesh: A B-spline finite cell method combined with level set function
Stress constrained shape and topology optimization with fixed mesh: A B-spline finite cell method combined with level set function
复制标题
固定网格应力约束形状与拓扑优化：结合水平集函数的B样条有限元方法
DOI：
10.1016/j.cma.2014.06.007
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发表时间：
2014-08
影响因子：
7.2
通讯作者：
Gao, Tong
中科院分区：
文献类型：
--
作者：
Cai, Shouyu;Zhang, Weihong;Zhu, Jihong;Gao, Tong
在本文中，我们开发了一种高效和灵活的设计方法，集成了B样条有限单元法（B样条FCM）和水平集函数（LSF）的应力约束形状和拓扑优化。任何复杂几何结构都嵌入在扩展的、规则的和固定的欧拉网格中，无论结构如何优化。为了保证应力分析和灵敏度分析的精度，进一步构造了高阶B样条形状函数。同时，水平集函数，即，隐式函数用于通过平滑边界变化实现所考虑的结构的拓扑变化。设计变量直接取所涉及的参数，而不是传统的离散形式的LSF，以方便数值计算过程。具体地说，LSF是通过R-函数，将三次样条作为隐式函数，以提供灵活性的形状优化的框架内的固定网格，而紧支撑径向基函数（CS-RBFs）被用作隐式函数的应力约束拓扑优化。结果表明，提出的FCM/LSF方法是一种方便的方法，可以计算应力和应力灵敏度与高精度。有代表性的形状和拓扑优化的例子，并没有应力约束的成功解决证明FCM/LSF方法的优点。
In this paper, we develop an efficient and flexible design method that integrates the B-spline finite cell method (B-spline FCM) and the level set function (LSF) for stress constrained shape and topology optimization. Any structure of complex geometry is embedded within an extended, regular and fixed Eulerian mesh no matter how the structure is optimized. High-order B-spline shape functions are further implemented to ensure precisions of stress analysis and sensitivity analysis. Meanwhile, level set functions, i.e., implicit functions are used to enable topological changes of the considered structure through smooth boundary variations. Involved parameters rather than the conventional discrete form of LSF are directly taken as design variables to facilitate the numerical computing process. To be specific, the LSF is constructed by means of R-functions that incorporate cubic splines as implicit functions to offer flexibilities for shape optimization within the framework of fixed mesh, while the compactly supported radial basis functions (CS-RBFs) are employed as implicit functions for stress constrained topology optimization. It is shown the proposed FCM/LSF method is a convenient approach that makes it possible to calculate stress and stress sensitivities with high precision. Representative examples of shape and topology optimization with and without stress constraints are solved with success demonstrating the advantages of the FCM/LSF method.
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DOI：
10.1016/j.advengsoft.2009.03.006
发表时间：
2007-04
期刊：
Adv. Eng. Softw.
影响因子：
--
作者：
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通讯作者：
J. París;F. Navarrina;I. Colominas;M. Casteleiro
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2000-08
影响因子：
2.9
作者：
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通讯作者：
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影响因子：
3.1
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影响因子：
3.9
作者：
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通讯作者：
J. París;F. Navarrina;I. Colominas;M. Casteleiro
DOI：
10.1016/j.cma.2008.02.036
发表时间：
2008-01-01
影响因子：
7.2
作者：
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通讯作者：
Rank, E.