Isogeometric Analysis-Based Topological Optimization for Heterogeneous Parametric Porous Structures

Porous structures widely exist in nature and artifacts, which can be exploited to reduce structural weight and material usage or improve damage tolerance and energy absorption. In this study, the authors develop an approach to design optimized porous structures with Triply Periodic Minimal Surfaces (TPMSs) in the framework of isogeometric analysis (IGA)-based topological optimization. In the developed method, by controlling the density distribution, the designed porous structures can achieve the optimal mechanical performance without increasing the usage of materials. First, the implicit functions of the TPMSs are adopted to design several types of porous elements parametrically. Second, to reduce the cost of computation, the authors propose an equivalent method to forecast the elastic modulus of these porous elements with different densities. Subsequently, the relationships of different porous elements between the elastic modulus and the relative density are constructed. Third, the IGA-based porous topological optimization is developed to obtain an optimal density distribution, which solves a volume constrained compliance minimization problem based on IGA. Finally, an optimum heterogeneous porous structure is generated based on the optimized density distribution. Experimental results demonstrate the effectiveness and efficiency of the proposed method.