Topology optimization for stationary fluid–structure interaction problems with turbulent flow via sequential integer linear programming and smooth explicit boundaries

数学优化 整数规划 流量(数学) 拓扑(电路) 湍流 拓扑优化 线性规划 数学 流体力学 计算机科学 应用数学 物理 机械 几何学 组合数学 有限元法 热力学
作者
Lucas Oliveira Siqueira,Rômulo Luz Cortez,Raghavendra Sivapuram,Shahin Ranjbarzadeh,Rafael dos Santos Gioria,Emílio Carlos Nelli Silva,Renato Picelli
出处
期刊:Advances in Engineering Software [Elsevier BV]
卷期号:190: 103599-103599
标识
DOI:10.1016/j.advengsoft.2024.103599
摘要

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 {0,1} 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 k−ɛ 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.
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