大规模三维制造容差应力约束拓扑优化
Large scale three-dimensional manufacturing tolerant stress-constrained topology optimization
摘要：
在拓扑优化中，由于鲁棒聚集方法的失败，即它们不能准确地处理应力约束的局部性，因此迄今为止对非常大规模问题的应力约束的处理还不容易处理。本文提出了一种三维设计方法，利用确定性和鲁棒性的问题配方来弥补这一缺点。基于三场密度投影方法，将鲁棒公式扩展到处理三维应力约束问题中的制造不确定性。几个数值算例的解决和进一步后处理与贴体网格使用商业软件。数值研究表明：（1）所采用的基于增广拉格朗日方法的求解方法能够处理具有数亿应力约束的大型问题;（2）如果采用适当的插值参数，基于体素的（固定网格）模型可用于计算冯·米塞斯应力，具有极好的精度;以及（3）为了在三维应力约束拓扑优化中确保制造公差，可能需要双重过滤和多于三个实现的组合。
英文摘要：
In topology optimization, the treatment of stress constraints for very large scale problems has so far not been tractable due to the failure of robust agglomeration methods, i.e. their inability to accurately handle the locality of the stress constraints. This paper presents a three-dimensional design methodology that alleviates this shortcoming using both deterministic and robust problem formulations. The robust formulation, based on the three-field density projection approach, is extended to handle manufacturing uncertainty in three-dimensional stress-constrained problems. Several numerical examples are solved and further post-processed with body-fitted meshes using commercial software. The numerical investigations demonstrate that: (1) the employed solution approach based on the augmented Lagrangian method is able to handle large problems, with hundreds of millions of stress constraints; (2) if appropriate interpolation parameters are adopted, voxel-based (fixed grid) models can be used to compute von Mises stresses with excellent accuracy; and (3) in order to ensure manufacturing tolerance in three-dimensional stress-constrained topology optimization, a combination of double filtering and more than three realizations may be required.
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