基于移动变形构件（MMC）和计算共形映射（CCM）的复杂曲面拓扑结构optimization
Topology optimization on complex surfaces based on the moving morphable component (MMC) method and computational conformal mapping (CCM)
摘要：
本文提出了一种求解具有任意亏格的复杂曲面拓扑优化问题的集成方法。该方法基于二维移动变形构件（MMC）框架和计算共形映射（CCM）技术，前者以一组结构构件作为优化的基本单元，后者将由非结构三角形网格表示的复杂曲面数值映射到一组规则的二维参数域。一个多补丁拼接计划也被开发，以实现MMC友好的全球参数化，通过一些局部参数化。通过对鞍形壳、圆环壳和三通管的数值算例验证了该方法的有效性。结果表明，与传统的二维曲面拓扑优化方法相比，该方法可以在较少的设计变量和有限元分析自由度的情况下，获得具有清晰载荷传递路径的优化设计。
英文摘要：
In the present paper, an integrated paradigm for topology optimization on complex surfaces with arbitrary genus is proposed. The approach is constructed based on the two-dimensional (2D) Moving Morphable Component (MMC) framework, where a set of structural components are used as the basic units of optimization, and computational conformal mapping (CCM) technique, with which a complex surface represented by an unstructured triangular mesh can be mapped into a set of regular 2D parameter domains numerically. A multi-patch stitching scheme is also developed to achieve an MMC-friendly global parameterization through a number of local parameterizations. Numerical examples including a saddle-shaped shell, a torus-shape shell and a tee-branch pipe are solved to demonstrate the validity and efficiency of the proposed approach. It is found that compared with traditional approaches for topology optimization on 2D surfaces, optimized designs with clear load transmission paths can be obtained with much fewer numbers of design variables and degrees of freedom for finite element analysis (FEA) via the proposed approach.
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