Topology optimization methods face serious challenges when applied to structural design with fluid–structure interaction (FSI) loads, especially for high Reynolds fluid flow, i.e., considering turbulence. In this problem, the information at the fluid–structure interface is crucial for the modeling and convergence of the turbulent fluid flow analysis. This paper devises a new explicit boundary method that generates two- and three-dimensional smooth surfaces to be used in topology optimization with binary design variables. A phase-field function is obtained after nodal spatial filtering of the design variables. The 0.5 isoline defines a smooth surface to construct the topology. The FSI problem can then be modeled with accurate physics and explicitly defined regions. The Finite Element Method is used to solve the fluid and structural domains. This is the first work to consider a turbulent flow in the fluid–structure topology optimization framework. The fluid flow is solved considering the turbulence model including standard wall functions at the fluid and fluid–structure boundaries. The structure is considered to be linearly elastic. Semi-automatic differentiation is employed to compute sensitivities and the optimization problem is solved via sequential integer linear programming. Results show that the proposed methodology is able to provide structural designs with smooth boundaries considering loads from low and high Reynolds flow.

中文翻译：

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通过顺序整数线性规划和平滑显式边界对湍流稳态流固耦合问题进行拓扑优化

当拓扑优化方法应用于具有流固耦合（FSI）载荷的结构设计时，特别是对于高雷诺流体流动（即考虑湍流）时，面临着严峻的挑战。在这个问题中，流固界面的信息对于湍流流体流动分析的建模和收敛至关重要。本文设计了一种新的显式边界方法，可生成二维和三维光滑表面，用于二元设计变量的拓扑优化。对设计变量进行节点空间滤波后获得相场函数。0.5 等值线定义了一个光滑表面来构建拓扑。然后可以使用精确的物理场和明确定义的区域对 FSI 问题进行建模。有限元法用于求解流体和结构域。这是第一个在流固拓扑优化框架中考虑湍流的工作。流体流动的求解考虑了湍流模型，包括流体和流体-结构边界处的标准壁函数。该结构被认为是线弹性的。采用半自动微分来计算灵敏度，并通过顺序整数线性规划解决优化问题。结果表明，考虑到低雷诺流和高雷诺流的载荷，所提出的方法能够提供具有平滑边界的结构设计。