A particle swarm optimization and coupled generalized differential quadrature element methods with genetic algorithm for stability analysis of the laminated microsystems

In this paper, an attempt is made to extend a linear two-dimensional model for stability analysis of the laminated annular microplate subject to external excitation. A new approach called hybrid optimization is introduced to solve optimization problems with a high sensitive objective function to decline computational costs and increase the predicted optimum results accuracy. Regarding this issue, generalized differential quadrature element method (GDQEM), particle swarm optimization (PSO), as well as genetic algorithm (GA) methods are coupled to improve the dynamic stability of the annular microsystems via finding an optimum frequency and fiber angle of layers simultaneously. Higher-order shear deformation theory (HSDT) and Hamilton’s principle are taken into consideration for the exact derivation of the general linear governing equations and boundary conditions of the axisymmetric laminated annular plate. Also, modified couple stress theory (MCST) is presented for presenting the size-dependency of the current microsystem. The GDQEM is used to solve the governing equations of the microsystem via its boundary domains. To enhance the genetic algorithms’ performance for solving equations, the optimizer approach of particle swarm has been employed as a GA’s operator. Precise convergence and practicality of the suggested mixed-method have been disclosed. Moreover, we would have proven that for achieving the convergence PSO’s and GA’s outcomes, we have to apply higher than fifteen iterations.