A multivariate level set method for concurrent optimization of graded lattice structures with multiple microstructure prototypes.

The concurrent optimization design of graded lattice structures (GLSs) considering both the diversity of microstructure prototypes and the geometric continuity has attracted extensive attention. This paper presents a multivariable level set-based topology optimization method for designing GLSs considering the matching of multiple microstructure prototypes. In this method, the basic level set functions (LSFs) of implicit and designable microstructures are constructed using the signed distance function. Multiple sets of LSFs are further developed by introducing weight coefficients to generate GLSs based on the basic LSFs. During optimization, each set of LSFs will generate a sub-GLS corresponding to the pre-defined microstructure prototype. Then, the final GLS containing multiple microstructures is obtained by combining these sub-GLSs through a union operation. Due to the continuity of the multivariable LSF, perfect geometric connections between neighboring graded microstructures are guaranteed without imposing any extra constraints. This work offers a novel strategy to optimize the macroscopic graded pattern of GLSs, resulting in an enlarged design space and performance improvement. Several 2D and 3D examples are presented to demonstrate the effectiveness and applicability of the proposed method. [ABSTRACT FROM AUTHOR]