A data-driven model of multiple variable cutting (M-VCUT) level set-based substructure is proposed for the topology optimization of lattice structures. The M-VCUT level set method is used to represent substructures, enriching their diversity of configuration while ensuring connectivity. To construct the data-driven model of substructure, a database is prepared by sampling the space of substructures spanned by several substructure prototypes. Then, for each substructure in this database, the stiffness matrix is condensed so that its degrees of freedom are reduced. Thereafter, the data-driven model of substructures is constructed through interpolation with compactly supported radial basis function (CS-RBF). The inputs of the data-driven model are the design variables of topology optimization, and the outputs are the condensed stiffness matrix and volume of substructures. During the optimization, this data-driven model is used, thus avoiding repeated static condensation that would require much computation time. Several numerical examples are provided to verify the proposed method.

A partition of unity level set method with moving knot Compactly Supported Radial Basis Functions (CS-RBFs) is proposed for optimizing variable stiffness composite structures. The iso-contours of a level set function are utilized to represent the curved fiber paths, and the tangent vector of the iso-contour defines the orientation of fiber. The level set function of the full design domain is constructed according to the Partition of Unity (POU) method by a set of local level set functions defined on an array of overlapping subdomains, and they are constructed by using the CS-RBFs. The positions of knots are iteratively changed during the optimization to improve the performance of composite structures. Several examples of compliance minimization are presented.