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.

中文翻译：

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具有多个微结构原型的梯度晶格结构并行优化的多元水平集方法

考虑微结构原型的多样性和几何连续性的梯度晶格结构（GLS）的并行优化设计引起了广泛的关注。本文提出了一种基于多变量水平集的拓扑优化方法，用于设计考虑多个微观结构原型匹配的 GLS。在该方法中，使用有符号距离函数构造隐式可设计微观结构的基本水平集函数（LSF）。在基本LSF的基础上，通过引入权重系数进一步发展多组LSF，生成GLS。在优化过程中，每组LSF将生成与预定义的微观结构原型相对应的子GLS。然后，通过联合操作将这些子GLS组合起来，得到包含多个微观结构的最终GLS。由于多变量LSF的连续性，保证了相邻渐变微观结构之间完美的几何连接，而无需施加任何额外的约束。这项工作提供了一种优化 GLS 宏观分级模式的新颖策略，从而扩大了设计空间并提高了性能。给出了几个 2D 和 3D 示例来证明该方法的有效性和适用性。