Fiber path optimization based on a family of curves in composite laminate with a center hole

A family of curves based fiber path optimization approach is developed to optimize the fiber paths in composite laminate with a centered hole, in an attempt to improve the uniaxial tensile load carrying capabilities. In the proposed optimization method, a novel family of curves with two design variables is assumed to approximate the fiber paths in composite laminate. The principal stress trajectories are chosen as the desired fiber paths in order to make full usage of the mechanical properties of continuous fibers. The objective function is constructed by the nonlinear weighted least squares method, taking the first principal stress components as the weights. Using the Trust-Region-Reflective algorithm, the design variables appeared in the family of curves can be optimized. Once the optimal design variables are obtained, consequently, the fiber paths are optimized. With the obtained optimal path results, a comparative study will be given by means of two laminates, the path optimized laminate and the unidirectional laminate. Four failure criteria will be used to evaluate the maximum strength indexes of the laminates under a uniaxial tensile load. From the finite element results, it is shown that the maximum strength indexes can be reduced by 19%-39% when using the fiber path optimized laminate. Meanwhile, the tensile testing results of these two laminates also agree well with the predicted maximum strength indexes.