The Darcy method for Topology Optimisation of pressure actuated compliant mechanisms

Abstract

This work introduces a new method to deal with design dependent pressure loads in Topology Optimisation (TO) using the SIMP material model. A pronounced focus is on optimising pressure actuated compliant mechanisms. The difficulty herein is the interpretation of the pressure boundary in a TO design. In TO the boundaries are blurry, because of the filtering of the design variables, which is necessary to prevent checkerboarding. Another reason why the boundary is poorly defined is that the optimisation starts from an equally distributed grey, where black and white respectively are solid and void, so the boundary is either the domain boundary or not defined in early iterations of the optimisation.
The methods proposed in literature often try to find the void-solid interface exposed to the pressure source to apply the loading from a pressure line directly. The method proposed in this work, appropriately called the Darcy method, first calculates the pressure field by using Darcy's law governing the flow through porous media and the associated pressure drop. A flow coefficient is introduced that decreases if the virtual element density increases. This results in a design dependent pressure field that can be solved using the Finite Element Method (FEM), which can then be translated to consistent nodal forces that are applied to the TO problem. A drainage coefficient has also been introduced to make sure that the pressure is drained entirely to the environment pressure over the first encountered void-solid interface exposed to the pressure source. The Darcy method has proven to function well in several test cases. The method has been thoroughly tested using several parameter sweeps on a clamping problem objective. The parameters whose influence is examined are: the initial condition, the density threshold value, flow coefficient gradient at the threshold, output spring stiffness and the volume fraction.
Subsequently, some alternative TO problems are solved showing the diversity of the method. In perspective of future research, the Darcy method can function as a great tool to research load sensitivities by tuning the pressure field control parameters. The extension of the Darcy method to 3D or to several load cases comes naturally but has not been tested in this work, this is also recommended for future research.