Evolutionary topology optimization of continuum structures with smooth boundary representation
Evolutionary topology optimization of continuum structures with smooth boundary representation
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DOI：
10.1007/s00158-017-1846-6
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发表时间：
2018-06
影响因子：
3.9
通讯作者：
D. Da;L. Xia;Guangyao Li;Xiaodong Huang
中科院分区：
文献类型：
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作者：
D. Da;L. Xia;Guangyao Li;Xiaodong Huang
提出了一种扩展的双向渐进结构优化（BESO）方法，用于光滑边界条件下连续体结构的拓扑优化。相对于传统的曲折BESO设计和删除/添加元素，新提出的进化拓扑优化（ETO）方法，隐含地确定了光滑的结构拓扑结构的水平集函数（LSF）构造的节点灵敏度数。建立了设计模型与有限元分析模型之间的投影关系。设计模型的分析由具有各种元素体积分数的FEA模型代替，这些元素体积分数由辅助LSF确定。灵敏度LSF的引入导致沿着FEA模型的固体-空隙界面的中间体积元素沿着，从而有助于设计模型的优化拓扑的更好收敛。一系列二维和三维拓扑优化设计问题验证了所提出方法的有效性和鲁棒性，包括柔度最小化和固有频率最大化。结果表明，所提出的ETO方法能够生成清晰、光滑的边界表示，同时所得到的设计结果对初始设计和有限元网格分辨率的依赖性较小。
This paper develops an extended bi-directional evolutionary structural optimization (BESO) method for topology optimization of continuum structures with smoothed boundary representation. In contrast to conventional zigzag BESO designs and removal/addition of elements, the newly proposed evolutionary topology optimization (ETO) method, determines implicitly the smooth structural topology by a level-set function (LSF) constructed by nodal sensitivity numbers. The projection relationship between the design model and the finite element analysis (FEA) model is established. The analysis of the design model is replaced by the FEA model with various elemental volume fractions, which are determined by the auxiliary LSF. The introduction of sensitivity LSF results in intermediate volume elements along the solid-void interface of the FEA model, thus contributing to the better convergence of the optimized topology for the design model. The effectiveness and robustness of the proposed method are verified by a series of 2D and 3D topology optimization design problems including compliance minimization and natural frequency maximization. It has been shown that the developed ETO method is capable of generating a clear and smooth boundary representation; meanwhile the resultant designs are less dependent on the initial guess design and the finite element mesh resolution.