面向增材制造各向异性的结构拓扑与打印方向协同优化

doi:10.3901/JME.2023.17.220

摘要/Abstract

摘要： 增材制造技术的快速发展为拓扑优化产生的复杂设计提供了一种有效的制造手段。然而，与传统制造方式相比，由增材制造逐层打印工艺获得的结构通常表现为具有各向异性的刚度和强度特性，经验性地选择优化结构的打印方向忽略了工艺的影响，严重限制增材制造结构性能。因此，提出一种结构拓扑与打印方向协同优化方法，用于各向异性材料模型下的构型及打印角设计，并通过改善各设计变量相互耦合导致的优化收敛不稳定问题，实现增材制造产品综合性能提升。首先，建立基于材料旋转角的各向异性等效刚度矩阵和基于Tsai-Hill失效准则的强度约束表达式。其次，引入拉格朗日乘数以同时考虑结构柔度与失效系数约束，并推导关于单元设计变量的灵敏度方程，以及开发权值混合方法进一步推导关于材料旋转角的解析解。最后，采用一系列数值算法及关键参数更新策略稳定优化历程。典型算例表明，所提方法可以有效地产生最佳拓扑结构和打印方向，在保证结构强度的同时显著提高刚度特性，且优化过程易于收敛。

关键词: 增材制造, 拓扑优化, 各向异性材料, 失效准则, 打印方向

Abstract: The rapid development of additive manufacturing (AM) technology provides an effective manufacturing method for complex designs generated by topology optimization. However, compared with traditional manufacturing methods, structures obtained by layer-by-layer printing process of AM usually exhibit anisotropic stiffness and strength properties, and the empirical selection of optimal structural print direction ignores the influence of process, which seriously limits the performance of AM structures. Therefore, a simultaneous optimization method of structural topology and print direction is proposed for the configuration and print angle design of anisotropic material model. The optimization convergence instability caused by coupling of design variables is improved to achieve the comprehensive performance improvement of AM products. Firstly, the anisotropic equivalent stiffness matrix based on material rotation angle and the strength constraint expression based on Tsai-Hill failure criterion are established. Secondly, the Lagrange multiplier is introduced to consider both structural compliance and failure coefficient constraint, and the sensitivity of the elemental design variables is derived. The weight hybrid method is developed to further derive the analytical solution of the material rotation angle. Finally, a series of numerical algorithms and key parameters updating strategies are used to stabilize the optimization process. The typical examples show that the proposed method can effectively obtain the optimized topology and optimal print direction. The final results significantly improve the stiffness while ensuring the structural strength, and the optimization process is easy to converge.

Key words: additive manufacturing, topology optimization, anisotropic material, failure criterion, print direction

中图分类号:

TH122

江和昕, 何智成, 周恩临. 面向增材制造各向异性的结构拓扑与打印方向协同优化[J]. 机械工程学报, 2023, 59(17): 220-231.

JIANG Hexin, HE Zhicheng, ZHOU Enlin. Simultaneous Optimization of Structural Topology and Print Direction for Additive Manufacturing Anisotropy[J]. Journal of Mechanical Engineering, 2023, 59(17): 220-231.

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