Topology optimization with local stress constraints: a stress aggregation-free approach
Topology optimization with local stress constraints: a stress aggregation-free approach
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DOI：
10.1007/s00158-020-02573-9
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发表时间：
2020-08
影响因子：
3.9
通讯作者：
Fernando V. Senhora;O. Giraldo-Londoño;I. Menezes;G. Paulino
中科院分区：
文献类型：
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作者：
Fernando V. Senhora;O. Giraldo-Londoño;I. Menezes;G. Paulino
本文通过增强拉格朗日方法提出了一种具有局部应力约束的质量最小化的一致拓扑优化公式。为了有效地解决具有大量约束的问题，我们修改了增广拉格朗日函数的惩罚项和目标函数项。惩罚项的修改导致网格细化下的一致解，目标函数项的修改推动质量最小化朝向黑白解。此外，我们引入了分段消失约束，其结果优于使用松弛应力约束获得的结果。尽管保持应力的局部性质需要大量应力约束，但此处提出的公式仅需要一个伴随向量，从而实现有效的灵敏度评估。提供了多个 2D 和 3D 拓扑优化问题，每个问题都具有大量局部应力约束。
This paper presents a consistent topology optimization formulation for mass minimization with local stress constraints by means of the augmented Lagrangian method. To solve problems with a large number of constraints in an effective way, we modify both the penalty and objective function terms of the augmented Lagrangian function. The modification of the penalty term leads to consistent solutions under mesh refinement and that of the objective function term drives the mass minimization towards black and white solutions. In addition, we introduce a piecewise vanishing constraint, which leads to results that outperform those obtained using relaxed stress constraints. Although maintaining the local nature of stress requires a large number of stress constraints, the formulation presented here requires only one adjoint vector, which results in an efficient sensitivity evaluation. Several 2D and 3D topology optimization problems, each with a large number of local stress constraints, are provided.