A parametric divergence-free vector field method for the optimization of composite structures with curvilinear fibers

Abstract

Benefiting from the progress of manufacturing technology of fiber-reinforced composite structures, the angle of a fiber is allowed to change continuously, and stiffness can be different at different positions of a structure. Therefore, the design optimization has large freedom to improve the performance of a structure. A fundamental issue in the design optimization is how to describe the spatially varying fiber angles. In the present study, the fiber angle arrangement is described by using a parametric divergence-free vector field (pDVF) that is constructed through an expansion by using a set of basis vector fields. A basis vector field is obtained by multiplying the gradient vectors of a compact supported radial basis function with an anti-symmetric matrix. Then the expansion coefficients are regarded as design variables in the optimization. The proposed method is able to describe continuous curvilinear fibers, and it ensures that the fibers in one ply do not cross each other.