Topology optimization applied to fluid–structure interaction problems is challenging because the physical phenomenon in real engineering applications is usually transient and strongly coupled. This leads to costly solutions for the forward and adjoint problems, the computational bottleneck of the topology optimization method. Thus, this paper proposes a topology optimization problem formulated in the steady state with post-processing and verification in the transient state. The objective is to design a stiff structure with lower effects of vibrations induced by the transient fluid vortices. For that, the compliance minimization problem is solved subject to a natural frequency constraint (without any volume constraint). The TOBS-GT (Topology Optimization of Binary Structures with geometry trimming) method is used to solve the problem. To observe the vortex-shedding around the structure, a transient simulation is performed considering an incompressible fluid flow under a laminar regime and the structure subject to large displacements. For topology optimization, the fluid flow is at a steady state and the structure is modeled considering small displacements, i.e., a one-way coupled analysis. The finite element method is used to solve the governing equations and obtain the direct/adjoint sensitivities for the compliance and natural frequency functions. In this approach, the natural frequency of the structure is shifted away from the fluid flow vortex-shedding frequency, avoiding resonance. Numerical examples show that the proposed method can be effectively applied to design 2D structures in FSI problems with lower effects of Flow-Induced Vibration, attenuating the levels of displacement at the analyzed points of the structure.

中文翻译：

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考虑涡激振动衰减固有频率约束的稳态流固耦合问题的拓扑优化

应用于流固耦合问题的拓扑优化具有挑战性，因为实际工程应用中的物理现象通常是瞬态且强耦合的。这导致前向和伴随问题（拓扑优化方法的计算瓶颈）的解决方案成本高昂。因此，本文提出了一种在稳态下表述并在瞬态下进行后处理和验证的拓扑优化问题。目标是设计一种刚性结构，以降低瞬态流体涡流引起的振动影响。为此，在固有频率约束（没有任何体积约束）的情况下解决了柔量最小化问题。TOBS-GT（带几何修剪的二元结构拓扑优化）方法用于解决该问题。为了观察结构周围的涡旋脱落，考虑层流状态下的不可压缩流体流动和承受大位移的结构进行瞬态模拟。对于拓扑优化，流体流动处于稳态，并且考虑小位移对结构进行建模，即单向耦合分析。采用有限元方法求解控制方程并获得柔度函数和固有频率函数的直接/伴随灵敏度。在这种方法中，结构的固有频率远离流体流动涡旋脱落频率，避免了共振。数值例子表明，所提出的方法可以有效地应用于流激振动影响较小的流激振动影响的二维结构设计，从而减弱结构分析点处的位移水平。