Topology Optimization of Fluidic Pressure Loaded Structures using the Biot-Darcy Method

Abstract

In many applications, design problems involving structures experience fluidic pressure loads. During topology optimization (TO) of such design problems, these loads adapt their direction and location with the evolution of the design, which poses various challenges. A novel approach to optimize a relaxed formulation of such design problems is presented to provide a continuous and consistent treatment of design-dependent pressure loads. Its effect is to allow for micro-perforated composite as admissible designs. The porosity of each finite element is related to its density variable using a regular function, yielding a smooth transition between the solid and void phases. A design-dependent pressure field is established using Biot-Darcy's law and the associated PDE is solved using the finite element method. The approach provides a computationally inexpensive evaluation of load sensitivities using the adjoint-variable method. Since it places no assumption on the number of holes cut within the domain, it can be seen as a topology optimization algorithm. Numerical results are presented for various two dimensional problems. We seek minimizers of the sum of the elastic compliance, fluid-elastic compliance and of the weight of a solid structure under fluidic pressure loads