Size-dependent optimal microstructure design based on couple-stress theory
Size-dependent optimal microstructure design based on couple-stress theory
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DOI：
10.1007/s00158-010-0484-z
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发表时间：
2010-02
影响因子：
3.9
通讯作者：
W. Su;Shutian Liu
中科院分区：
文献类型：
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作者：
W. Su;Shutian Liu
本文的目的是基于有效偶应力连续体模型，提出一种周期性蜂窝材料微结构的尺寸相关拓扑优化公式。目前的公式包括寻找材料的最佳布局，在允许的材料体积分数的约束下，使宏观结构的平均柔度最小化。我们通过基于应变能等效性的代表体积元（RVE）方法分析具有指定边界条件的晶胞来确定有效的宏观力偶应力本构常数。采用有限元（FE）方法建立计算模型，并通过固体各向同性材料惩罚幂（SIMP）定律将RVE的设计密度和FE刚度联系起来。还导出了基于梯度的优化算法所需的灵敏度公式。数值示例表明，本公式可以表达优化过程中的尺寸效应，并提供精确的拓扑结构，而不会增加计算成本。
The purpose of this paper is to propose a size-dependent topology optimization formulation of periodic cellular material microstructures, based on the effective couple-stress continuum model. The present formulation consists of finding the optimal layout of material that minimizes the mean compliance of the macrostructure subject to the constraint of permitted material volume fraction. We determine the effective macroscopic couple-stress constitutive constants by analyzing a unit cell with specified boundary conditions with the representative volume element (RVE) method, based on equivalence of strain energy. The computational model is established by the finite element (FE) method, and the design density and FE stiffness of the RVE are related by the solid isotropic material with penalization power (SIMP) law. The required sensitivity formulation for gradient-based optimization algorithm is also derived. Numerical examples demonstrate that this present formulation can express the size effect during the optimization procedure and provide precise topologies without increase in computational cost.