The optimization of porous infill structures via local volume constraints has become a popular approach in topology optimization. In some design settings, however, the iterative optimization process converges only slowly, or not at all even after several hundreds or thousands of iterations. This leads to regions in which a distinct binary design is difficult to achieve. Interpreting intermediate density values by applying a threshold results in large solid or void regions, leading to sub-optimal structures. We find that this convergence issue relates to the topology of the stress tensor field that is simulated when applying the same external forces on the solid design domain. In particular, low convergence is observed in regions around so-called trisector degenerate points. Based on this observation, we propose an automatic initialization process that prescribes the topological skeleton of the stress field into the material field as solid simulation elements. These elements guide the material deposition around the degenerate points, but can also be remodelled or removed during the optimization. We demonstrate significantly improved convergence rates in a number of use cases with complex stress topologies. The improved convergence is demonstrated for infill optimization under homogeneous as well as spatially varying local volume constraints.

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多孔填充优化的应力拓扑分析

通过局部体积约束优化多孔填充结构已成为拓扑优化中的一种流行方法。然而，在某些设计环境中，迭代优化过程收敛速度很慢，甚至在经过数百或数千次迭代后也完全不收敛。这导致难以实现独特的二元设计的区域。通过应用阈值来解释中间密度值会产生大的实心或空洞区域，从而导致次优结构。我们发现这个收敛问题与在实体设计域上施加相同外力时模拟的应力张量场的拓扑有关。特别是，在所谓的三等分退化点周围的区域中观察到低收敛。基于这一观察，我们提出了一个自动初始化过程，将应力场的拓扑骨架作为实体模拟元素指定到材料场中。这些元素引导退化点周围的材料沉积，但也可以在优化过程中重新建模或移除。我们在具有复杂应力拓扑的许多用例中展示了显着提高的收敛速度。在均匀和空间变化的局部体积约束下，为填充优化证明了改进的收敛性。我们在具有复杂应力拓扑的许多用例中展示了显着提高的收敛速度。在均匀和空间变化的局部体积约束下，为填充优化证明了改进的收敛性。我们在具有复杂应力拓扑的许多用例中展示了显着提高的收敛速度。在均匀和空间变化的局部体积约束下，为填充优化证明了改进的收敛性。