论文标题
大型三维制造耐应力约束拓扑优化
Large scale three-dimensional manufacturing tolerant stress-constrained topology optimization
论文作者
论文摘要
在拓扑优化中，由于强大的聚集方法的失败，即无法准确处理应力限制的位置，因此到目前为止对非常大规模问题的应力限制的处理尚未易于处理。本文提出了一种三维设计方法，可以使用确定性和健壮的问题表述来减轻这种缺点。基于三场密度投影方法的稳健配方被扩展为处理三维应力约束问题中的制造不确定性。使用商业软件解决了几个数值示例，并通过车身构造的网格进行了进一步的后处理。数值研究表明：（1）基于增强拉格朗日方法的使用的解决方案方法能够处理大型问题，并具有数亿个压力约束； （2）如果采用了适当的插值参数，则基于体素的（固定网格）模型可用于以极好的精度计算von Mises应力； （3）为了确保三维应力约束拓扑优化的制造耐受性，可能需要双重滤波和超过三个实现的组合。
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.
