一种高效且易于扩展的三维拓扑结构移动变形分量（MMC）方法的Matlab代码optimization
An efficient and easy-to-extend Matlab code of the Moving Morphable Component (MMC) method for three-dimensional topology optimization
摘要：
显式拓扑最优化方法近年来受到越来越多的关注。具体地，Zhang等人发布了基于二维（2D）移动可变形组件（MMC）的拓扑最优化方法的188行Matlab代码（Struct Multi Morphable Optim 53（6）：1243-1260，2016）。本工作的目的是提出一个有效的和易于扩展的256行Matlab代码的MMC方法的三维（3D）拓扑优化实施一些新的数值技术。具体地说，通过函数聚合技术，实现了精确的灵敏度分析，该方法也易于推广到其它问题。此外，基于一种有效的载荷传递路径识别算法，在有限元分析中去除了不属于载荷传递路径的自由度，大大加快了优化过程。结果表明，与相应的188行二维程序相比，优化结果的性能、有限元分析的计算效率、优化过程的收敛速度和鲁棒性都有很大提高。为了完整起见，还提供了实现2D-MMC方法的精炼的218行Matlab代码。
英文摘要：
Explicit topology optimization methods have received ever-increasing interest in recent years. In particular, a 188-line Matlab code of the two-dimensional (2D) Moving Morphable Component (MMC)-based topology optimization method was released by Zhang et al. (Struct Multidiscip Optim 53(6):1243-1260, 2016). The present work aims to propose an efficient and easy-to-extend 256-line Matlab code of the MMC method for three-dimensional (3D) topology optimization implementing some new numerical techniques. To be specific, by virtue of the function aggregation technique, accurate sensitivity analysis, which is also easy-to-extend to other problems, is achieved. Besides, based on an efficient identification algorithm for load transmission path, the degrees of freedoms (DOFs) not belonging to the load transmission path are removed in finite element analysis (FEA), which significantly accelerates the optimization process. As a result, compared to the corresponding 188-line 2D code, the performance of the optimization results, the computational efficiency of FEA, and the convergence rate and the robustness of optimization process are greatly improved. For the sake of completeness, a refined 218-line Matlab code implementing the 2D-MMC method is also provided.
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