This study proposes a novel topology optimization approach for design of continuous steering fiber path for composite structures using a level set method. The radial basis function (RBF) is employed to construct the level set function (LSF). Fiber orientations are parameterized by LSF and fiber paths can be determined instinctively for the inherent advantages of the level set approach. Besides, the fast-marching method is employed to extrapolate the primary fiber paths to the secondary fiber paths, which can avoid the manufacturing drawbacks such as gaps and overlaps to a large extent. A detection and filtering technique is proposed here to alleviate the orientation disorder at the intersection of the diffusion surfaces. Two design schemes are developed to optimize both structural topology and fiber path. In a sequential procedure, topology optimization is conducted first with isotropic materials; and then fiber paths are optimized on the basis of fixed topological boundary. In a simultaneous optimization procedure, structural boundaries and fiber paths are optimized alternately through two inner loops. In this study, three numerical examples are presented to demonstrate the effectiveness of the proposed methods, and the results show that optimization of fiber path is beneficial to improvement of structural performance. In general, the simultaneous optimization scheme exhibits better optimal outcome in comparison with the sequential optimization scheme.

本研究提出了一种新的拓扑优化方法，用于使用水平集方法设计复合结构的连续转向纤维路径。径向基函数（RBF）用于构造水平集函数（LSF）。纤维方向由 LSF 参数化，并且纤维路径可以根据水平集方法的固有优势本能地确定。此外，采用快速行进的方法将主光纤路径外推到次级光纤路径，可以在很大程度上避免间隙和重叠等制造缺陷。这里提出了一种检测和过滤技术，以减轻扩散表面相交处的取向紊乱。开发了两种设计方案来优化结构拓扑和光纤路径。在顺序过程中，首先使用各向同性材料进行拓扑优化；然后在固定拓扑边界的基础上优化光纤路径。在同步优化过程中，结构边界和光纤路径通过两个内环交替优化。在这项研究中，通过三个数值例子证明了所提出方法的有效性，结果表明优化光纤路径有利于提高结构性能。一般来说，与顺序优化方案相比，同步优化方案表现出更好的优化结果。