Topology optimization of fluidic pressure-loaded structures and compliant mechanisms using the Darcy method

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.

On topology optimization of design‐dependent pressure‐loaded three‐dimensional structures and compliant mechanisms

“…In this subsection, first the Darcy‐based pressure projection formulation is summarized, following our earlier 2D paper 5 . The Darcy law which determines a pressure field through a porous medium is employed.…”

“…The drainage coefficient is determined using a smooth Heaviside function such that pressure drops to zero for an FE with as where and are the adjustable parameters, and is defined analogous to Equation (3). The drainage coefficient of a solid FE, d s , is used to control the thickness of the pressure‐penetration layer and is related to K s as Reference 5 where r is the ratio of input pressure at depth s, that is, . Furthe...…”

“…The latter situation often arises in case of aerodynamic loads, hydrodynamic loads and/or hydrostatic pressure loads, in various applications including aircraft, pumps, ships, and pneumatically actuated soft robotics 2‐4 . Many TO methods exist for the former loading scenarios, whereas only few methods considering design‐dependent loading behaviors have been reported in TO 5 . Design‐dependent loads alter their location, direction, and/or magnitude as optimization progresses and thus, pose unique challenges 6 .…”

“…Fuchs and Shemesh 20 used a set of variables to define the pressure‐loaded boundary explicitly, in addition to the design variables, and they also optimized pressure load variables during optimization. For an overview of 2D pressure‐loaded TO approaches for designing structures and/or CMs, we refer to our recent paper on this subject 5 …”

“…In order to combine effectiveness in 3D CM designs under pressure loads, ease of implementation, and accuracy of load sensitivities, we herein extend the method presented by Kumar et al 5 to 3D design problems involving both structures and mechanisms. With this, we confirm the expectation expressed in our earlier study that the method can be naturally extended to 3D.…”