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Topology optimization of structures subject to non-Newtonian fluid–structure interaction loads using integer linear programming
Finite Elements in Analysis and Design ( IF 3.1 ) Pub Date : 2022-01-17 , DOI: 10.1016/j.finel.2021.103690
S. Ranjbarzadeh 1 , R. Picelli 2 , R. Gioria 2 , E.C.N. Silva 1
Affiliation  

This paper proposes a topology optimization design method for fluid–structure interaction (FSI) problems considering Non-Newtonian fluid such as blood and polymer solution. Non-Newtonian fluid does not obey the Newtonian relationship between the shear stress and shear rate. Fluid–structure interaction involving Non-Newtonian fluid has a wide range of application in oil and gas, chemical, food industries, microfluidics, and bio-engineering. We solve a compliance minimization problem subject to volume constraints of structures under FSI loads considering Non-Newtonian laminar flow. The structure is considered to undergo small deformation. The TOBS (Topology Optimization of Binary Structures) method is applied to solve the material distribution problem. The TOBS approach uses binary {0,1} design variables, which can be advantageous when dealing with design-dependent physics interactions, e.g., in cases where fluid–structure boundaries are allowed to change during optimization. The finite elements method is used to solve the fluid–structure equations and output the sensitivities using automatic differentiation. The TOBS optimizer provides a new set of {0,1} variables at every iteration. Optimization results show that Non-Newtonian effects have a significant influence on FSI design.



中文翻译:

使用整数线性规划对非牛顿流固耦合载荷下的结构进行拓扑优化

本文提出了一种考虑血液和聚合物溶液等非牛顿流体的流固耦合(FSI)问题的拓扑优化设计方法。非牛顿流体不服从剪切应力和剪切速率之间的牛顿关系。涉及非牛顿流体的流固耦合在油气、化工、食品工业、微流体和生物工程等领域有着广泛的应用。我们在考虑非牛顿层流的情况下解决了受 FSI 载荷下结构体积约束的顺应性最小化问题。该结构被认为发生了小变形。TOBS(二元结构拓扑优化)方法用于解决材料分布问题。TOBS 方法使用二进制{0,1}设计变量,这在处理与设计相关的物理相互作用时可能是有利的,例如,在优化过程中允许改变流体结构边界的情况下。有限元法用于求解流固耦合方程,并使用自动微分输出灵敏度。TOBS 优化器提供了一组新的{0,1}每次迭代的变量。优化结果表明,非牛顿效应对 FSI 设计有显着影响。

更新日期:2022-01-17
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