Symplectic Superposition-Based Analytical Solutions for Buckling of Non-Lévy-Type Orthotropic Cylindrical Shells

LIU Mingfeng; XU Dian; NI Zhuofan; LI Yihao; LI Rui

doi:10.21656/1000-0887.440093

Volume 44 Issue 12

Dec. 2023

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Article Navigation > Applied Mathematics and Mechanics > 2023 > 44(12): 1428-1440

LIU Mingfeng, XU Dian, NI Zhuofan, LI Yihao, LI Rui. Symplectic Superposition-Based Analytical Solutions for Buckling of Non-Lévy-Type Orthotropic Cylindrical Shells[J]. Applied Mathematics and Mechanics, 2023, 44(12): 1428-1440. doi: 10.21656/1000-0887.440093

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Symplectic Superposition-Based Analytical Solutions for Buckling of Non-Lévy-Type Orthotropic Cylindrical Shells

doi: 10.21656/1000-0887.440093

State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Received Date: 2023-04-03
Rev Recd Date: 2023-04-25
Publish Date: 2023-12-01

Abstract

Abstract

Based on the symplectic superposition method (SSM) pioneered by the authors, the buckling problem of typical non-Lévy-type orthotropic cylindrical shells was solved analytically, which is difficult to handle with conventional analytical methods. The Hamiltonian system-based governing equations for buckling of orthotropic cylindrical shells were firstly established based on Donnell's shell theory. The original problem under non-Lévy-type boundary conditions was then divided into 2 subproblems, and each subproblem was solved with the mathematical techniques incorporating separation of variables and symplectic eigen expansion within the Hamiltonian framework. The analytical solution of the original problem was finally given through the superposition of the sub-solutions to satisfy the boundary conditions of the original problem. The numerical examples under consideration show that, the SSM-based analytical solutions are in good agreement with the finite element results. In addition, the effects of parameters including the length and the thickness on the critical buckling loads were quantitatively studied. Compared with the conventional analytical methods such as the semi-inverse method, the SSM works based on rigorous mathematical derivation without any assumption of the solution forms, and can obtain reliable analytical solutions to more similar issues.
- orthotropic,
- cylindrical shell,
- buckling,
- symplectic superposition method,
- analytical solution

(Contributed by LI Rui, M.AMM Editorial Board)

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References(26)

References

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