Abstract We propose a new algorithm to design lightweight and stiff structures exhibiting free-form features, with the aim of minimizing the compliance under a volume inequality constraint. The procedure is based on the coupling of geometric shape optimization with topology optimization. We start from a full-mass body corresponding to a given material occupying entirely the initial design domain. The first phase of geometric shape optimization acts as an out-of-the-box paradigm. It allows one to modify the initial design domain by acting only on its boundary, keeping the same volume and topology. With respect to the full-mass body, this phase reduces the compliance to a large extent. The successive step of topology optimization does actually change the topology of the structure, e.g., by introducing holes, reduces the volume according to the volume constraint, but does not affect the boundary of the structure, which is fixed by the previous phase. Overall, the combined approach allows us to design a new structure, that is lighter and stiffer with respect to the full-mass body. Additionally, the employment of a structure-tailored computational mesh, via an anisotropic mesh adaptation procedure during topology optimization, yields an intrinsically smooth final layout characterized by free-form features. An extensive numerical assessment corroborates both qualitatively and quantitatively the performances of the proposed optimization algorithm.

中文翻译：

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一种自动结构设计的优化算法

摘要 我们提出了一种新算法来设计具有自由形状特征的轻质刚性结构，目的是在体积不等式约束下最小化柔顺性。该过程基于几何形状优化与拓扑优化的耦合。我们从与完全占据初始设计域的给定材料相对应的全质量物体开始。几何形状优化的第一阶段充当开箱即用的范例。它允许人们通过仅作用于其边界来修改初始设计域，保持相同的体积和拓扑。对于全质量体，该阶段在很大程度上降低了顺应性。拓扑优化的后续步骤实际上改变了结构的拓扑，例如，通过引入孔洞，根据体积约束减小体积，但不影响结构边界，该边界由前一阶段固定。总的来说，组合方法使我们能够设计一种新结构，相对于全质量车身更轻、更硬。此外，在拓扑优化过程中，通过各向异性网格自适应程序采用结构定制的计算网格，产生以自由形式特征为特征的本质上平滑的最终布局。广泛的数值评估定性和定量地证实了所提出的优化算法的性能。与全质量车身相比，它更轻、更硬。此外，在拓扑优化过程中，通过各向异性网格自适应程序采用结构定制的计算网格，产生以自由形式特征为特征的本质上平滑的最终布局。广泛的数值评估定性和定量地证实了所提出的优化算法的性能。与全质量车身相比，它更轻、更硬。此外，在拓扑优化过程中，通过各向异性网格自适应程序采用结构定制的计算网格，产生以自由形式特征为特征的本质上平滑的最终布局。广泛的数值评估定性和定量地证实了所提出的优化算法的性能。