This work presents a systematic optimization method utilizing non-uniform rational B-splines (NURBS) to represent fibers in composites and design their paths. Beyond mean compliance, the objective function incorporates repulsive energy to prevent fiber knots and intersections. Utilizing NURBS control points as design variables reduces the number of design variables and expands the solution space, as they can reach any point within the design domain under the guidance of the sensitivity of the objective function in the method of moving asymptotes. Additionally, the p-norm technique for curvature constraints represents an innovative adaptation to avoid sharp turns in fibers. The work can also add fibers during optimization and enable the design of multi-layer fiber-enhanced composite structure to address various design challenges associated with optimizing fiber paths. Numerical examples show that the mean compliance decreases by 60∼70 % compared to initial configurations, and the computation time is reduced by 80 % compared to similar cases in prior work.

中文翻译：

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基于非均匀有理 B 样条 (NURBS) 的光纤路径设计优化方法

这项工作提出了一种利用非均匀有理 B 样条 (NURBS) 来表示复合材料中的纤维并设计其路径的系统优化方法。除了平均顺应性之外，目标函数还包含排斥能量以防止纤维打结和交叉。利用NURBS控制点作为设计变量，在移动渐近线方法中目标函数敏感性的指导下，可以到达设计域内的任意点，减少了设计变量的数量，扩大了解空间。此外，用于曲率约束的 p 范数技术代表了一种创新的适应方法，可以避免光纤中的急转弯。这项工作还可以在优化过程中添加纤维，并实现多层纤维增强复合材料结构的设计，以解决与优化纤维路径相关的各种设计挑战。数值例子表明，与初始配置相比，平均柔度降低了 60∼70%，与先前工作中的类似情况相比，计算时间减少了 80%。