A novel fiber optimization method based on normal distribution function with continuously varying fiber path

Tailoring fiber orientation has been a very interesting approach to improve the efficiency of composite structures. For the discrete angle selection approach, previous methods use formulations that requires many variables, increasing the computational cost, and they cannot guarantee total fiber convergence (which is the selection of only one candidate angle). This paper proposes a novel fiber orientation optimization method based on the optimized selection of discrete angles, commonly used to avoid the multiple local minima problem found in fiber orientation optimization methods that consider the fiber angle as the design variable. The proposed method uses the normal distribution function as the angle selection function, which requires only one variable to select the optimized angle among any number of discrete candidate angles. By adjusting a parameter in the normal distribution function, total fiber convergence can be achieved. In addition, a usual problem in fiber angle optimization methods is that because fibers can be arbitrarily oriented, structural problems may exist at the intersection of discontinuous fiber paths. Besides, composite manufacturing technologies, such as Advanced Fiber Placement (AFP), produce better results when fiber paths are continuous. These problems can be avoided by considering continuously varying fiber paths. In the proposed method, fiber continuity is also achieved by using a spatial filter, which improves the fiber path and avoids structural problems. Numerical examples are presented to illustrate the proposed method.