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 Structural Engineering and Mechanics   Volume 87, Number 5, September10 2023 , pages 461-473 DOI: https://doi.org/10.12989/sem.2023.87.5.461 A semi-analytical and numerical approach for solving 3D nonlinear cylindrical shell systems Liming Dai and Kamran Foroutan Abstract This study aims to solve for nonlinear cylindrical shell systems with a semi-analytical and numerical approach implementing the P-T method. The procedures and conditions for such a study are presented in practically solving and analyzing the cylindrical shell systems. An analytical model for a nonlinear thick cylindrical shell (TCS) is established on the basis of the stress function and Reddy's higher-order shear deformation theory (HSDT). According to Reddy's HSDT, Hooke's law in three dimensions, and the von-Kármán equation, the stress-strain relations are developed for the thick cylindrical shell systems, and the three coupled nonlinear governing equations are thus established and discretized as per the Galerkin method, for implementing the P-T method. The solution generated with the approach is continuous everywhere in the entire time domain considered. The approach proposed can also be used to numerically solve and analyze the nonlinear shell systems. The procedures and recurrence relations for numerical solutions of shell systems are presented. To demonstrate the application of the approach in numerically solving for nonlinear cylindrical shell systems, a specific nonlinear cylindrical shell system subjected to an external excitation is solved numerically. In numerically solving for the system, the present approach shows higher efficiency, accuracy, and reliability in comparison with that of the Runge-Kutta method. The approach with the P-T method presented is practically sound especially when continuous and high-quality numerical solutions for the shell systems are considered. Key Words 3D nonlinear vibration; cylindrical shells; P-T method; Reddy's HSDT; reliability and accuracy; Runge-Kutta method Address Liming Dai and Kamran Foroutan: Sino-Canada Research Centre of Computation and Mathematics, Qinghai Normal University and the University of Regina, Qinghai Normal University, China; Industrial Systems Engineering, University of Regina, Regina, SK, S4S 0A2, Canada

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