Design of laminated conical shells using spectral Chebyshev method and lamination parameters

This study presents a modeling approach to accurately and efficiently predict the dynamics of laminated conical shells. The governing equations are derived based on the first order shear deformation theory kinematic equations following the Hamilton's principle. To express the strain energy of the shells, in-plane and bending lamination parameters are used. A two-dimensional spectral approach based on Chebyshev polynomials is implemented to solve the governing equations. The developed framework including the spectral-Chebyshev approach and lamination parameters results in an accurate and computationally efficient solution method. To demonstrate the performance of the presented solution approach, various case studies including straight panels, curved shells, and truncated conical shells are investigated. The benchmarks indicate that the calculated non-dimensional natural frequencies excellently match the results found using finite element method and the simulation duration can be decreased by 100 folds. To leverage the computational performance of the presented approach, a stacking sequence optimization is performed to maximize the fundamental frequency of a shell geometry, and the corresponding fiber angles are retrieved from the optimized lamination parameters. Furthermore, a parametric analysis is performed to investigate the effect of geometry on the optimized lamination parameters (and fiber angles) based on fundamental natural frequency maximization.