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陈卓, 龙凯, 张承婉, 杨晓宇, 刘鑫. 多节点位移约束拓扑优化的增广拉格朗日法[J]. 计算机辅助设计与图形学学报, 2023, 35(3): 474-481. DOI: 10.3724/SP.J.1089.2023.19364
引用本文: 陈卓, 龙凯, 张承婉, 杨晓宇, 刘鑫. 多节点位移约束拓扑优化的增广拉格朗日法[J]. 计算机辅助设计与图形学学报, 2023, 35(3): 474-481. DOI: 10.3724/SP.J.1089.2023.19364
Chen Zhuo, Long Kai, Zhang Chengwan, Yang Xiaoyu, and Liu Xin. The Augmented Lagrangian Method for Topology Optimization Subject to Multiple Nodal Displacement Constraints[J]. Journal of Computer-Aided Design & Computer Graphics, 2023, 35(3): 474-481. DOI: 10.3724/SP.J.1089.2023.19364
Citation: Chen Zhuo, Long Kai, Zhang Chengwan, Yang Xiaoyu, and Liu Xin. The Augmented Lagrangian Method for Topology Optimization Subject to Multiple Nodal Displacement Constraints[J]. Journal of Computer-Aided Design & Computer Graphics, 2023, 35(3): 474-481. DOI: 10.3724/SP.J.1089.2023.19364

多节点位移约束拓扑优化的增广拉格朗日法

The Augmented Lagrangian Method for Topology Optimization Subject to Multiple Nodal Displacement Constraints

  • 摘要: 针对结构承载面抗变形的设计需求,提出增广拉格朗日框架下的多节点位移约束拓扑优化方法.首先,建立以多节点位移为约束、以体积分数最小化为目标的拓扑优化列式;其次,利用增广拉格朗日方法将数量众多的位移约束方程转化到目标函数中,将多约束优化问题转化为无约束优化问题;最后,采用移动渐进线法求解无约束优化问题.数值算例结果表明,与包络函数方法相比,该方法能够进一步减少结构体积,且具有稳健、高效和不受参数影响的优势;与柔顺度最小化列式相比,该方法能够有效地控制局部区域的变形,在如风电叶片结构轻量化设计等工程应用中具有必要性.

     

    Abstract: To address the design requirements of deformation resistance of structural load-bearing surfaces, a multiple nodal displacement constraint topology optimization method is proposed in the augmented Lagrangian framework. Firstly, a topological optimization formulation is established, with multiple nodal displacement as the constraints and volume fraction minimization as the objective. Secondly, the multi-constrained optimization problem is subsequently transformed into an unconstrained optimization problem by converting numerous displacement constraint functions into the objective function by the augmented Lagrangian method. Finally, the unconstrained optimization problem is then solved using the method of moving asymptotes. Numerical results demonstrate that, when compared to the aggregation method, the proposed method is more robust, efficient, and parameter-independent. By comparison with formulation for compliance minimization, the proposed method can effectively control deformation in the local region, which is critical for engineering applications such as lightweight design of wind turbine blades.

     

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