Generalized differential quadrature element solution, swarm, and GA optimization technique to obtain the optimum frequency of the laminated rotary nanostructure

Abstract

Optimization of the fiber angle in the laminated composite material to achieve the highest strength or stability has great importance in structural design. In the present study, we aim to utilize genetic algorithm (GA) and particle swarm optimization (PSO) together to find the best angle of composite layers in a multilayer cylindrical shell structure. To this aim, a detailed formulation of the composite cylindrical structure is presented using nonlocal strain gradient theory (NSGT), zigzag theory, and Hamilton's principle for a shear deformable shell displacement field. The modal equations of motion are further solved using the general differential quadrature element method (GDQEM). Having the route of obtaining the resonance frequency of the cylindrical composite structure, GA-PSO is engaged to obtain the optimal angle of the laminate composite to achieve the highest frequency. It is revealed that angle θ = 37.5° provides the highest frequency for a single-layer cylindrical shell. Using this angle, stacking sequences for 3, 5, and 7 layers’ composite are optimized to have the highest frequency. In the end, a detailed parametric study is presented using optimum condition shell composite. The results show that after 30 composite layers, changing the number of layers seems to be not effective on the resonance frequency of the cylinder for both simply supported and clamped boundary conditions.