Design for the Maximum Natural Frequency of Laminated Composite Plates by Optimally Distributed Short Fibers

Abstract

A new design method is proposed for vibration of functional fibrous composite plates, which imitate micro structures of natural materials such as bones and shells. The material has local anisotropy induced by optimally distributed short fibers which are defined in each element of the finite element method. To design such locally anisotropic plates, the present optimum design method combines a genetic algorithm method (GA) with a layerwise optimization (LO) concept. The LO concept reduces a multi-layer optimization into iterations of a single-layer optimization, and the GA is used for the single-layer optimization to determine fiber orientation angles in each element. The fundamental frequency of the plates is chosen as the objective function to be maximized. It was revealed that the present plates give higher fundamental frequencies than conventional plates reinforced by parallel straight fibers. Further optimally distributed short fibers indicated specific orientations even though no constraint was imposed on those directions.

Natural frequencies and vibration modes of laminated composite plates reinforced with arbitrary curvilinear fiber shape paths

“…Frequencies are strongly affected by the boundary conditions and it is known that ±45° fiber orientation angles are shapes suitable to the simply supported edge [13]. The present plates with (i) quasi-quadratic and (iii) arbitrary fibers have ±45° fiber shapes adjacent to the left and right edges.…”

“…Expecting to obtain similar effects with continuous curvilinear fibers, the present authors [12,13] have studied the optimization problem of short fiber distributions in laminated fibrous composite plates in order to minimize the maximum deflection and to maximize the fundamental frequency of the plate. The optimum lamination parameter distributions obtained from Ref.…”

“…The optimum lamination parameter distributions obtained from Ref. [12] were calculated at each element in the finite element analysis (FEA) simultaneously using a gradient method, and the optimum short fiber distributions were thereby determined in each element by using the angle determination method from the lamination parameters which were proposed elsewhere [14,15]. Further, combining a genetic algorithm [16] and a layerwise optimization concept [17,18] solved the natural frequency maximization problem effectively [13].…”

Multi-objective optimization of curvilinear fiber shapes for laminated composite plates by using NSGA-II

“…Van Campen et al, recently, proposed a method for generating fiber shapes [16]. The authors here also used lamination parameters to design optimum short fiber distributions [17]. Blom et al [18,19] designed conical shells using curvilinear fibers for maximizing fundamental frequencies while imposing manufacturing constraints, and optimized fiber paths using stream line analogy.…”