We present a novel method for computational design of adaptive shape-memory alloy (SMA) structures via topology optimization. By optimally distributing a shape-memory alloy within the prescribed design domain, the proposed algorithm seeks to tailor the two-way shape memory effect (TWSME) and pseudoelasticity response of the SMA materials. Using a phenomenological material model, the thermomechanical response of the SMA structure is solved through inelastic finite element analysis, while assuming a transient but spatially uniform temperature distribution. The material distribution is parameterized via a SIMP formulation, with gradient-based optimization used to perform the optimization search. We derive a transient, bi-level adjoint formulation for analytically computing the design sensitivities. We demonstrate the proposed design framework using a series of two-dimensional thermomechanical benchmark problems. These examples include design for optimal displacement due to the two-way shape memory effect, and design for maximum mechanical advantage while accounting for pseudoelasticity.

中文翻译：

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使用瞬态双级伴随方法优化形状记忆合金结构的热机械拓扑

我们提出了一种通过拓扑优化计算设计自适应形状记忆合金 (SMA) 结构的新方法。通过在规定的设计域内优化分布形状记忆合金，所提出的算法旨在调整 SMA 材料的双向形状记忆效应 (TWSME) 和伪弹性响应。使用现象学材料模型，通过非弹性有限元分析求解 SMA 结构的热机械响应，同时假设瞬态但空间均匀的温度分布。材料分布通过 SIMP 公式进行参数化，并使用基于梯度的优化来执行优化搜索。我们推导出一个瞬态、双层伴随公式，用于分析计算设计灵敏度。我们使用一系列二维热机械基准问题演示了所提出的设计框架。这些示例包括由于双向形状记忆效应而设计的最佳位移，以及在考虑伪弹性的同时实现最大机械优势的设计。