We introduce an efficient method for designing shell reinforcements of minimal weight. Inspired by classical Michell trusses, we create a reinforcement layout whose members are aligned with optimal stress directions, then optimize their shape minimizing the volume while keeping stresses bounded. We exploit two predominant techniques for reinforcing shells: adding ribs aligned with stress directions and using thicker walls on regions of high stress. Most previous work can generate either only ribs or only variable-thickness walls. However, in the general case, neither approach by itself will provide optimal solutions. By using a more precise volume model, our method is capable of producing optimized structures with the full range of qualitative behaviors: from ribs to walls and smoothly transitioning in between. Our method includes new algorithms for determining the layout of reinforcement structure elements, and an efficient algorithm to optimize their shape, minimizing a non-linear non-convex functional at a fraction of the cost and with better optimality compared to standard solvers. We demonstrate the optimization results for a variety of shapes and the improvements it yields in the strength of 3D-printed objects.

中文翻译：

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一般壳结构的加固

我们介绍了一种设计重量最小的外壳加强件的有效方法。受经典 Michell 桁架的启发，我们创建了一个钢筋布局，其成员与最佳应力方向对齐，然后优化它们的形状以最小化体积，同时保持应力有界。我们利用两种主要的技术来加固外壳：添加与应力方向对齐的肋和在高应力区域使用较厚的壁。大多数以前的工作要么只生成肋骨，要么只生成可变厚度的墙。然而，在一般情况下，这两种方法本身都不能提供最佳解决方案。通过使用更精确的体积模型，我们的方法能够生成具有全方位定性行为的优化结构：从肋骨到墙壁以及在两者之间平滑过渡。我们的方法包括用于确定加固结构元素布局的新算法，以及优化其形状的有效算法，以极少的成本最小化非线性非凸函数，并且与标准求解器相比具有更好的最优性。我们展示了各种形状的优化结果以及它对 3D 打印物体强度的改进。