Topology optimization of structures subject to non-Newtonian fluid–structure interaction loads using integer linear programming

• Published in: Finite elements in analysis and design Vol. 202; p. 103690
• Main Authors: Ranjbarzadeh, S., Picelli, R., Gioria, R., Silva, E.C.N.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.05.2022; Elsevier BV
• Subjects: Binary design variables; Bioengineering; Design optimization; Finite element method; Finite elements method; Fluid-structure interaction; Integer programming; Laminar flow; Linear programming; Microfluidics; Newtonian fluids; Non Newtonian fluids; Non-Newtonian fluid; Optimization; Shear rate; Shear stress; TOBS method; Topology optimization; Topology optimization; Fluid–structure interaction; TOBS method; Finite elements method; Binary design variables; Non-Newtonian fluid
• ISSN: 0168-874X; 1872-6925
• DOI: 10.1016/j.finel.2021.103690

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. •A novel topology optimization method is developed for fluid–structure interaction problems.•Fluid–structure boundaries are allowed to change during optimization.•The TOBS (Topology Optimization of Binary Structures) method is applied to solve the material distribution problem.•Optimization results show that Non-Newtonian effects have a significant influence on FSI design.