Minimization of stress concentration for laminated composite plates with curvilinearly shaped fibers

Abstract

The equivalent stress concentration of laminated composite plates reinforced by curvilinear fibers is minimized with respect to fiber geometries under uniaxial tensile load. Projection of contour lines in cubic-polynomial is used to represent curvilinear geometry of fibers, and this description makes it possible to tolerate multi-valued function without solving simultaneous equations, typically seen in the process of using the spline function. The finite element method is employed with the eight-node quadrilateral isoparametric element for stress concentration analysis. In this FEM procedure, curvilinear fibers are approximated by assuming straight short fibers in each element. The optimum curvilinear fiber shapes are searched for minimizing the equivalent stress concentration using a simple genetic algorithm, and the coefficients of terms in cubic polynomial are used as design variables. In numerical examples, single-layer and angle-ply laminated composite plates are considered for different aspect ratios of circular holes. The optimized results show that the present plates with optimally shaped curvilinear fibers can make the equivalent stress concentration lower than those of the conventional plates with optimally oriented parallel fibers.