中图分类号： TH122 文献标志码：A

Topology optimization design method of shape memory alloy structure

CHEN Shitong， DING Xiaohong， XIONG Min （SchoolofMechanical Engineering， UniversityofShanghai for Scienceand TechnologyShanghai 2ooo93，China）

Abstract： Based on the superelastic properties exhibited by shape memory alloy， a cosine type constitutive model and a solid isotropic material penalty model were combined to describe the characteristics of shape memory alloy. A material interpolation function was established and a variable density topology optimization method was used to achieve structural topology optimization design considering the nonlinearity of shape memory alloy. The proposed method was applied to design the typical two-dimensional and three-dimensional structures. Static analysis and martensitic transformation evolution analysis were used to analysis the structure obtained by the proposed optimization method.

The results show that the structure optimized by the proposed method has beter mechanical properties compared to the traditional one. In static analysis， the maximum internal stress decreases by 19.57% and the maximum displacement decreases by 31.03% . In the analysis of martensitic transformation evolution， the maximum volume fraction of martensite at the end of loading decreases by 20.27% . The proposed optimization design method results in the even overal stress distribution within the structure， less prone to local stress concentration， and less deformation caused by martensitic transformation.

Keywords： shape memory aloy; topology optimization; structure design; material nonlinearity; Martensitic transformation evolution

形状记忆合金作为一种新型的智能材料，在航空航天、生物医疗等领域都取得了广泛的应用。与不锈钢、铸铁等传统的线弹性金属材料相比，形状记忆合金的显著特性是在外部温度和力学刺激下发生奥氏体相和马氏体相的无扩散固态相变。这种相变往往伴随着高达 6%～8% 的可恢复弹性形变以及材料属性的变化，这类非线性材料特性通常被称为形状记忆效应或超弹性[1]。鉴于这一独特的材料性质，形状记忆合金被广泛应用于多个领域。王奇等[2将形状记忆合金丝组合布置在机翼后缘上下关节铰链处，通过加热触发形状记忆效应，带动铰链关节部分实现机翼后缘结构的偏转，设计了机翼后缘的智能可控变形结构。戴剋戎等[3使用镍钛基形状记忆合金制作了骨折环抱器，这种环抱器利用形状记忆效应，使环抱臂变形并抱紧骨断端两侧，实现了对断骨的固定。Boroschek等[4利用形状记忆合金受力学刺激发生超弹性变形时会消耗大量能量的滞回特性，制作了形状记忆合金阻尼器，将形状记忆合金丝嵌人到刚性框架结构中，并引入振动台进行测试。结果表明，相比原始框架结构，带阻尼结构的峰值相对位移减少了 30%～60% ，峰值加速度减少了近 58% 。

结构优化设计指通过改变结构的几何尺寸、形状或排列以及材料分布等方式，改善结构在载荷工况下的负载表现，从而提升结构性能的一种设计方法[5]。常见的结构优化设计方法有尺寸优化、形状优化、拓扑优化等。……