Generating Curvilinear Fiber Paths from Lamination Parameters Distribution

Abstract

Contrary to the classical stacking sequence design of composite laminates with straight fibers, each ply can be designed with curvilinear fiber paths resulting in variation of the stiffness properties over the structure. Such laminates are often denoted as “variablestiffness panels” in the literature. Instead of treating fiber orientation angles as spatial design variables, lamination parameters can be used. However, retrieving the actual stacking sequence requires additional efforts at a post processing level. In this paper, we presume that the optimal distribution of lamination parameters is already obtained for a particular design problem. Then we use curve fitting techniques to obtain continuous fiber paths that result in a distribution of the lamination parameters close to the optimal distribution in a least square sense while satisfying the manufacturing curvature constraint. The fiber orientation angle is expanded using a set of basis functions and unknown coefficients. The unknown coefficients are then computed such t hat the assumed form represents the optimal distribution of the lamination parameters in a least square sense. The key feature of such approach is that at this post-processing step, no more expensive finite element analyses are needed and the curve fitting is performed using simple polynomial and trigonometric function evaluations. The curve fitting problem is then solved using a constrained nonlinear least square solver where maximum curvature is controlled using a side constraint. Numerical results demonstrate the efficiency of the proposed formulation for minimum compliance design problems. For the cantilever plate problem investigated, the compliance of the approximate design is only than 2.5% larger than than the compliance of optimal lamination parameters design. A methodology is also proposed to estimate the thickness buildup due to the curved fiber paths.