Topology optimization of fluidic pressure-loaded structures and compliant mechanisms using the Darcy method
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RESEARCH PAPER
Topology optimization of fluidic pressure-loaded structures and compliant mechanisms using the Darcy method P. Kumar1,2
· J. S. Frouws2 · M. Langelaar2
Received: 24 August 2019 / Revised: 17 October 2019 / Accepted: 22 October 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In various applications, design problems involving structures and compliant mechanisms experience fluidic pressure loads. During topology optimization of such design problems, these loads adapt their direction and location with the evolution of the design, which poses various challenges. A new density-based topology optimization approach using Darcy’s law in conjunction with a drainage term is presented to provide a continuous and consistent treatment of design-dependent fluidic pressure loads. The porosity of each finite element and its drainage term are related to its density variable using a Heaviside function, yielding a smooth transition between the solid and void phases. A design-dependent pressure field is established using Darcy’s law and the associated PDE is solved using the finite element method. Further, the obtained pressure field is used to determine the consistent nodal loads. The approach provides a computationally inexpensive evaluation of load sensitivities using the adjoint-variable method. To show the efficacy and robustness of the proposed method, numerical examples related to fluidic pressure-loaded stiff structures and small-deformation compliant mechanisms are solved. For the structures, compliance is minimized, whereas for the mechanisms, a multi-criteria objective is minimized with given resource constraints. Keywords Topology optimization · Pressure loads · Darcy’s law · Stiff structures · Compliant mechanisms
1 Introduction In the last three decades, various topology optimization (TO) methods have been presented, and most have meanwhile attained a mature state. In addition, their popularity as design tools for achieving solutions to a wide variety of problems involving single/multi-physics is growing consistently. Among these, design problems involving fluidic
Responsible Editor: Jianbin Du P. Kumar
[email protected] M. Langelaar [email protected] 1
Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
2
Department of Precision and Microsystems Engineering, Delft University of Technology, 2628CD Delft, Netherlands
pressure loads1 pose several unique challenges, e.g., (i) identifying the structural boundary to apply such loads, (ii) determining the relationship between the pressure loads and the design variables, i.e., defining a design-dependent and continuous pressure field, and (iii) efficient calculation of the pressure load sensitivities. Such problems can be encountered in various applications (Hammer and Olhoff 2000) such as air-, water- and/or snow-loaded civil and mechanical structures (aircraft, pumps, pressure containers, ships, turbomachinery), pneumatically or hydraulically actuated soft r
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