Matlab code for a level set-based topology optimization method using a reaction diffusion equation
Matlab code for a level set-based topology optimization method using a reaction diffusion equation
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DOI：
10.1007/s00158-014-1190-z
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发表时间：
2015-05-01
影响因子：
3.9
通讯作者：
Nishiwaki, Shinji
中科院分区：
文献类型：
--
作者：
Otomori, Masaki;Yamada, Takayuki;Nishiwaki, Shinji
提出了一种基于水平集的拓扑优化方法的简单Matlab实现方法，该方法使用反应扩散方程更新水平集函数，这与传统的基于水平集的方法（Allaire et al. 2002，2004; Wang et al. 2003）不同，后者使用Hamilton-Jacobi方程更新水平集函数。该方法通过适当地设置正则化参数，可以很容易地控制优化构形的几何复杂性。我们详细解释了代码，也是推导的拓扑导数，这是用于基于水平集的拓扑优化。最后给出了刚度最大化问题的数值结果，以便于读者理解。本代码仅用于教育目的。本文的灵感来自于以前发表的论文，这些论文介绍了SIMP方法的Matlab代码（Sigmund 2001; Andreassen et al. 2011），基于水平集的方法（查利斯2010）和结构优化方法的FreeFem ++代码（Allaire and Pantz 2006）。读者可以调查这些不同方法提供的结果，并发现每个特定方法的突出方面。这里提供的代码可以从http://www.osdel.me.kyoto-u.ac.jp/members/yamada/codes.html下载。
This paper presents a simple Matlab implementation for a level set-based topology optimization method in which the level set function is updated using a reaction diffusion equation, which is different from conventional level set-based approaches (Allaire et al. 2002, 2004; Wang et al. 2003) that use the Hamilton-Jacobi equation to update the level set function. With this method, the geometrical complexity of optimized configurations can be easily controlled by appropriately setting a regularization parameter. We explain the code in detail, and also the derivation of the topological derivative that is used in the level set-based topology optimization. Numerical results for stiffness maximization problems are provided to facilitate the reader's understanding. The presented code is intended for educational purposes only. This paper was inspired by previously published papers presenting Matlab code for a SIMP method (Sigmund 2001; Andreassen et al. 2011), a level set-based method (Challis 2010), and FreeFem ++ code for a structural optimization method (Allaire and Pantz 2006). Readers can investigate results provided by these different methods and discover the prominent aspects of each particular method. The code presented here can be downloaded from http://www.osdel.me.kyoto-u.ac.jp/members/yamada/codes.html.