A topology optimization method based on the level set method incorporating a fictitious interface energy
A topology optimization method based on the level set method incorporating a fictitious interface energy
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DOI：
10.1016/j.cma.2010.05.013
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发表时间：
2010-01-01
影响因子：
7.2
通讯作者：
Takezawa, Akihiro
中科院分区：
文献类型：
--
作者：
Yamada, Takayuki;Izui, Kazuhiro;Takezawa, Akihiro
本文提出了一种新的拓扑优化方法，该方法利用Level Set方法并结合从相场法得到的虚拟界面能来调整最优构型的几何复杂性。首先，基于水平集方法建立了一个拓扑优化问题，并说明了通过引入虚拟界面能使优化问题正则化的方法。其次，推导了更新水平集函数的反应扩散方程，并构造了优化算法，在更新水平集函数时利用有限元方法求解平衡方程和反应扩散方程。最后，给出了几个优化设计实例，验证了所提出的拓扑优化方法的有效性和实用性。(C)2010爱思唯尔B.V.保留所有权利。
This paper proposes a new topology optimization method, which can adjust the geometrical complexity of optimal configurations, using the level set method and incorporating a fictitious interface energy derived from the phase field method. First, a topology optimization problem is formulated based on the level set method, and the method of regularizing the optimization problem by introducing fictitious interface energy is explained. Next, the reaction-diffusion equation that updates the level set function is derived and an optimization algorithm is then constructed, which uses the finite element method to solve the equilibrium equations and the reaction-diffusion equation when updating the level set function. Finally, several optimum design examples are shown to confirm the validity and utility of the proposed topology optimization method. (C) 2010 Elsevier B.V. All rights reserved.