Extended multiscale FEM-based concurrent optimization of three-dimensional graded lattice structures with multiple microstructure configurations

In this work, a novel concurrent design method for three-dimensional graded lattice structures considering multiple microstructure configurations is proposed. Firstly, the Multiple Variable Cutting (M-VCUT) level set method is employed to represent the geometry of lattice microstructures and define the optimization parameters. Then, the extended multiscale finite element method (EMsFEM) is implemented for calculating the equivalent stiffness matrices of microstructures in offline form. Compared with the traditional homogenization- based multiscale approaches, the proposed method eliminates the scale separation assumptions and takes into account the coupling effects in different directions of materials. In addition, a data-driven method and a parallel computing approach are integrated together so that computational efficiency can be greatly improved. After the iteration process, the optimized full-scale graded structures are reconstructed using interpolation technology to generate well-connected microstructures in neighboring cells. Finally, several 3D numerical examples are utilized to validate the effectiveness of the proposed method, where multiple lattice microstructure configurations are considered, including truss-lattices and plate-lattices.