Global Optimization of Stacking Sequence in a Laminated Cylindrical Shell Using Differential Quadrature Method

Abstract

Based on 3-D elasticity approach, differential quadrature method (DQM) in axial direction is adopted along with Globalized Nelder–Mead (GNM) algorithm to optimize the stacking sequence of a laminated cylindrical shell. The anisotropic cylindrical shell has finite length with simply supported boundary conditions. The elasticity approach, combining the state space method and DQM is used to obtain a relatively accurate objective function. Shell thickness is fixed and orientations of layers change in a set of angles. The partial differential equations are reduced to ordinary differential equations with variable coefficients by applying DQM to the equations, then, the equations with variables at discrete points are obtained. Natural frequencies are attained by solving the Eigen-frequency equation, which appears by incorporating boundary conditions into the state equation. A GNM algorithm is devised for optimizing composite lamination. This algorithm is implemented for maximizing the lowest natural frequency of cylindrical shell. The results are presented for stacking sequence optimization of two to five-layered cylindrical shells. Accuracy and convergence of developed formulation is verified by comparing the natural frequencies with the results obtained in the literature. Finally, the effects of mid-radius to thickness ratio, length to mid-radius ratio and number of layers on vibration behavior of optimized shell are investigated. Results are compared with those of Genetic Algorithm (GA) method, showing faster and more accurate convergence.