This paper presents a parametric level set method for the optimization of composite structures with curvilinear fibers. We use iso-contours of a scalar function, also called the level set function, to represent the fibers, and the level set function is constructed by a set of radial basis functions with compact support. The orientation of fiber at any arbitrary point is defined by the orientation of the tangent vector of iso-contour. In order to prevent gaps and overlaps between neighboring fiber tows from arising during the manufacturing of composite structures, a constraint is formulated that the norm of gradient vector of the level set function is equal to 1 almost everywhere. Furthermore, these gradient constraints are aggregated into a single one by using the $p$-norm method to improve the efficiency of optimization. The compliance minimization problem is considered, and the coefficients of radial basis functions are taken as the design variables. The results of optimizations proved that the proposed method can provide an optimized composite structure with equally spaced curvilinear fibers.

本文提出了一种用于优化具有曲线纤维的复合结构的参数化水平集方法。我们使用标量函数的iso-contours，也称为水平集函数，来表示纤维，水平集函数由一组紧支撑的径向基函数构成。纤维在任意点的取向由 iso-contour 的切线矢量的取向定义。为了防止在复合结构制造过程中相邻纤维束之间出现间隙和重叠，制定了一个约束条件，即水平集函数的梯度向量范数几乎处处等于1。此外，这些梯度约束通过使用$磷$-norm 方法来提高优化的效率。考虑了柔量最小化问题，以径向基函数的系数作为设计变量。优化结果证明所提出的方法可以提供具有等距曲线纤维的优化复合结构。