Topology optimization with supershapes
Topology optimization with supershapes
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DOI：
10.1007/s00158-018-2034-z
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发表时间：
2018-07
影响因子：
3.9
通讯作者：
Julián A. Norato
中科院分区：
文献类型：
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作者：
Julián A. Norato
这项工作提出了一种基于连续体的结构拓扑优化方法，其中结构由超形联合表示。超形状是超椭圆的延伸，它可以表现出可变的对称和不对称，并且可以通过一个方程（所谓的超公式）来描述各种各样的形状，包括几何基元。正如作者和他的合作者以及其他人在之前的工作中所证明的那样，基于特征的几何描述的可用性打开了施加几何约束的可能性，否则难以在基于密度或基于水平集的方法中施加几何约束。此外，这种描述可以直接翻译为计算机辅助设计系统。这项工作是作者小组之前工作的延伸，在那里，它希望描述结构的离散几何元素具有固定的形状（但尺寸可变），以便设计由库存材料制成的结构，如棒和板。超形的使用提供了一个更一般的几何描述，使用一个单一的公式，可以呈现一个结构完全由几何原语的联合。保留现有方法的标志性优势也是可取的，即能够使用固定网格进行分析，以避免重新划分网格，以及使用鲁棒和有效的基于梯度的优化方法的灵敏度。超形的几何表示和固定分析离散化之间的通道，如在先前的工作中一样，是将超形参数映射到密度场的可微几何投影。该方法在二维顺应性拓扑优化的经典问题上得到了验证。
This work presents a method for the continuum-based topology optimization of structures whereby the structure is represented by the union of supershapes. Supershapes are an extension of superellipses that can exhibit variable symmetry as well as asymmetry and that can describe through a single equation, the so-called superformula, a wide variety of shapes, including geometric primitives. As demonstrated by the author and his collaborators and by others in previous work, the availability of a feature-based description of the geometry opens the possibility to impose geometric constraints that are otherwise difficult to impose in density-based or level set-based approaches. Moreover, such description lends itself to direct translation to computer aided design systems. This work is an extension of the author’s group previous work, where it was desired for the discrete geometric elements that describe the structure to have a fixed shape (but variable dimensions) in order to design structures made of stock material, such as bars and plates. The use of supershapes provides a more general geometry description that, using a single formulation, can render a structure made exclusively of the union of geometric primitives. It is also desirable to retain hallmark advantages of existing methods, namely the ability to employ a fixed grid for the analysis to circumvent re-meshing and the availability of sensitivities to use robust and efficient gradient-based optimization methods. The conduit between the geometric representation of the supershapes and the fixed analysis discretization is, as in previous work, a differentiable geometry projection that maps the supershapes parameters onto a density field. The proposed approach is demonstrated on classical problems of 2-dimensional compliance-based topology optimization.