应用数学和力学2023，Vol.44Issue(12)：1428-1440,13.DOI:10.21656/1000-0887.440093
非Lévy型正交各向异性开口圆柱壳屈曲问题的辛叠加解析解
Symplectic Superposition-Based Analytical Solutions for Buckling of Non-Lévy-Type Orthotropic Cylindrical Shells
摘要
Abstract
Based on the symplectic superposition method(SSM)pioneered by the authors,the buckling prob-lem 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 ortho-tropic 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 superposi-tion of the sub-solutions to satisfy the boundary conditions of the original problem.The numerical examples un-der 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.关键词
正交各向异性/开口圆柱壳/屈曲/辛叠加方法/解析解Key words
orthotropic/cylindrical shell/buckling/symplectic superposition method/analytical solution分类
力学引用本文复制引用
刘明峰,徐典,倪卓凡,李逸豪,李锐..非Lévy型正交各向异性开口圆柱壳屈曲问题的辛叠加解析解[J].应用数学和力学,2023,44(12):1428-1440,13.基金项目
国家自然科学基金项目(12022209 （）
11972103) （）
