Design of topology-optimized functionally graded porous structures under transient loads

This paper presents a novel approach for designing functionally graded porous structures (FGPSs) at a macroscopic scale, where the main goal is to maximize their stiffness when subjected to time varying loads. Topology optimization is used to achieve the complex task of designing the size, shape, and distribution of pores in porous structures. We employ a local volume constraint that smoothly varies in space, leading to the formation of a graded structure consisting of varying sizes and shapes of solid and empty regions. Further constraints, such as global volume and static compliance, are incorporated into the optimization framework to improve the results. The modified solid isotropic material with penalization (SIMP) model is applied to interpolate the material properties. The design variables are filtered, and the projection technique is employed to obtain black-and-white topologies. The method of moving asymptotes (MMA) solves the optimization problem, which is a gradient-based algorithm. Sensitivities are computed using the adjoint variable method (AVM) within the discretize-then-differentiate strategy. The linear elastodynamic problem resulting from the transient finite element analysis (FEA) is solved with the implicit Newmark-$\beta$ scheme. Several numerical examples are provided to demonstrate the effectiveness of the proposed approach in producing multiple closed- and open-cell composite foams tailored to specific design criteria. The optimized FGPSs have the potential to fulfill the requirements for both lightweight and energy absorption in applications subjected to dynamic loads, such as those found in the automotive, aerospace and biomedical industries.