Abstract

In this work, the Huber-Hencky-Von Mises criterion for isotropic materials is integrated into a special density-based algorithm for topology optimization (TO). The algorithm makes use of (a) Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces to represent the pseudo-density field describing the topology of the continuum and (b) the well-known Solid Isotropic Material with Penalization approach. The local behavior and the singularity of stresses are efficiently handled thanks to the NURBS blending functions properties and a suitable aggregation function. To this end, a dedicated strategy is proposed to properly update the parameters governing the behavior of the aggregation function during the iterations of the optimization process. Moreover, the gradient of the criterion is derived in closed form (in the most general case when both displacements and forces are applied as boundary conditions) by exploiting the local support property of NURBS entities. A sensitivity analysis of the optimized topology to the integer parameters of the NURBS hyper-surface is carried out. Furthermore, a manufacturing requirement related to the minimum allowable size is also integrated into the problem formulation. The effectiveness of the approach is proven on 2 D and 3 D benchmark problems taken from the literature.

摘要

在这项工作中，各向同性材料的 Huber-Hencky-Von Mises 准则被集成到一种特殊的基于密度的拓扑优化 (TO) 算法中。该算法利用 (a) 非均匀有理基样条 (NURBS) 超曲面来表示描述连续体拓扑的伪密度场和 (b) 著名的带惩罚方法的固体各向同性材料。由于 NURBS 混合函数属性和合适的聚合函数，局部行为和应力的奇异性得到了有效处理。为此，提出了一种专用策略，以在优化过程的迭代过程中正确更新控制聚合函数行为的参数。而且，通过利用 NURBS 实体的局部支撑属性，以封闭形式（在最一般的情况下，当位移和力都作为边界条件应用时）导出准则的梯度。进行了优化拓扑对NURBS超曲面整数参数的敏感性分析。此外，与最小允许尺寸相关的制造要求也被整合到问题公式中。该方法的有效性在文献中的 2D 和 3D 基准问题上得到了证明。与最小允许尺寸相关的制造要求也被整合到问题公式中。该方法的有效性在文献中的 2D 和 3D 基准问题上得到了证明。与最小允许尺寸相关的制造要求也被整合到问题公式中。该方法的有效性在文献中的 2D 和 3D 基准问题上得到了证明。