Homogenization based topology optimization of fluid-pressure loaded structures using the Biot–Darcy Model

Abstract

The ambition to develop simulation methods making it possible to predict the integrity or the properties of use (mechanical, diffusive, thermal, electromagnetic, vibratory, etc.) of structures (industrial or natural), materials or processes involved in the development of new advanced technologies is growing consistently. In a global context of permanent development of advanced technologies (notably in the field of energy) and a growing need for cost reduction, the development times for new concepts are increasingly reduced and therefore tend to exclude monolithic design of multiphysic structures. Here, we propose an homogenization based topology optimization method to design multi-scale and multiphysic structures experiencing fluid-pressure loads. Its effect is to allow for micro-perforated composite as admissible designs, where the design is characterized by the material density and its homogenized Hooke's law at each point of the working space, yielding composite designs made of fine mixture between the solid and void phases. The fluid-pressure loads is determined using Biot-Darcy's law and solved using the finite element method. This approach permits a computationally low cost of evaluation of of load sensitivities using the Lagrangian method. As no assumption is impose on the number of micro-perforation inside the solid domain, this method can be seen as a topology optimization algorithm. We seek minimizers of the elastic compliances, fluid-elastic compliances and of the weight of a solid structure under fluid-pressure loads.