Hierarchical structure optimization with parameterized lattice and multiscale finite element method

In this work, a novel concurrent optimization framework based on multiscale finite element method is proposed to pursue superior-performance hierarchical structures with parameterized lattice. Distinguished with conventional homogenization-based optimization method, this framework gets rid of the assumption of scale separation while optimizing hierarchical structures. Firstly, a multi-parameter description is presented to generate a family of parameterized lattice cells that share similar geometric features. In order to balance structural performance and computational cost, we decompose the optimization framework into offline and online stages. In the offline stage, the equivalent stiffness matrix of lattice is calculated with the help of multiscale finite element method. A surrogate model based on general regression neural network (GRNN) is established to map lattice parameters to equivalent stiffness matrix. Besides, the discrete topological variables are introduced to determine the distribution of lattice. Discrete material optimization (DMO) model is employed to integrate such two kinds of design variables into a material interpolation model. Hence, the concurrent optimization framework can optimize the macroscopic distribution and their spatially varying lattice configurations simultaneously at an affordable computation cost. Finally, numerical examples are presented to illustrate the effectiveness of the proposed concurrent optimization framework, indicating that lattice size, relative density, and configuration have essential impacts on the hierarchical structural design and performance.