Topology Optimization of Fluidic Pressure Loaded Structures and Compliant Mechanisms using the Darcy Method

TL;DR

This paper introduces a novel density-based topology optimization method using Darcy's law to effectively handle design-dependent fluidic pressure loads in structures and compliant mechanisms, ensuring smooth transitions and computational efficiency.

Contribution

It presents a new approach combining Darcy's law with a drainage term for continuous treatment of fluidic loads in topology optimization, improving robustness and efficiency.

Findings

Successfully applied to fluidic pressure loaded structures and mechanisms

Achieves smooth transition between solid and void phases

Provides computationally inexpensive load sensitivity evaluation

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.