Hierarchical topology optimization considering design-dependent pressure loads

Fluid-induced pressures usually alter in magnitude, direction, and application points during the action, which requires sophisticated computational modeling. Furthermore, multiscale design parameters have strong interdependencies. For the first time, this paper presents a comprehensive investigation on the hierarchical topology optimization considering pressure loads. In this framework, a smooth transition between solids and voids is achieved using the classical solid isotropic material penalization method with Heaviside function, Darcy's law and a drainage term are adopted to construct an ideal natural pressure field. The homogenization method builds a bridge between macroscopic and microscopic structural optimization. The macro-structural design variables are updated using the moving asymptotes method, to address the challenge in the case of non-unique monotonicity of the sensitivity information, and the micro-structural design variables are updated by using the optimality criteria method. Hierarchical topology optimization under pressure loads was demonstrated across varying pressure loads, dimensional scales, and volume constraints. The calculation results show that the pressure loads will have significant impacts on the topological configurations and numerical results of the hierarchical structures, and the calculation time under pressure loads is 10 to 20 times longer than the optimization time under fixed loads. Notably, microscopic configurations differ substantially between 2D and 3D implementations.