The superior stiffness-to-weight and strength-to-weight mechanical advantages of sandwich structures can be fully exploited through concurrent design of entire topology, infill configuration and density, where the high-performance yet complicated structure can be fabricated through additive manufacturing. However, the emerging design challenges are concurrent design updating related to sandwich topology, infill configuration and density, which is a design problem with continuous and discrete variables mathematically. In this paper, a concurrent topology optimization is proposed for sandwich structures with multi-configuration and variable-diameter lattice infill. Three design variable fields are employed to describe the fundamental topology considering sandwich structural topology, infill configuration and density simultaneously. Corresponding material interpolation model is developed by combining DSP-based shell-infill description and multi-response latent-variable surrogate model based effective material property calculation. Two-stage design model is formulated as a rough design model considering all design variables followed by a refined design model with only infill density variables, which is developed to strictly satisfy the material allowance constraint due to the mapping between discrete infill configuration variables and continuous latent configuration variables. Corresponding sensitivities of compliance and constraint with respect to the structural topology, infill configuration and density variables are derived, and the method of moving asymptotes (MMA) is employed to solve the design model efficiently. Several numerical examples are presented to systematically demonstrate the effectiveness of the proposed approach.

中文翻译：

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具有多配置和可变直径晶格填充的夹层结构的并行拓扑优化


夹层结构卓越的刚度重量比和强度重量比机械优势可以通过整个拓扑、填充配置和密度的并行设计得到充分利用，其中高性能但复杂的结构可以通过增材制造制造。然而，新出现的设计挑战是与三明治拓扑、填充配置和密度相关的并发设计更新，这是一个数学上具有连续和离散变量的设计问题。在本文中，针对具有多构型和可变直径晶格填充的夹层结构提出了一种并行拓扑优化。采用三个设计变量字段来描述同时考虑夹层结构拓扑、填充结构和密度的基本拓扑。结合基于 DSP 的壳填充描述和基于多响应潜在变量代理模型的有效材料性能计算，开发了相应的材料插值模型。两阶段设计模型被表述为考虑所有设计变量的粗略设计模型，然后是仅具有填充密度变量的精细设计模型，该模型被开发为严格满足由于离散填充配置变量和连续潜在配置变量之间的映射而导致的材料余量约束。推导了结构拓扑、填充构型和密度变量方面相应的柔度和约束敏感性，并采用移动渐近线 （MMA） 的方法对设计模型进行有效求解。提出了几个数值示例，以系统地证明了所提出的方法的有效性。