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Z = the Batdorf parameter
Z = sqrt(1-nu^2)L^2/(Rt)
nu=Poisson ratio; L=length; R=radius; t=thickness
Fig.4 Buckling modes under various boundary conditions, C1, C2, C3, C4 (“clamped type” b.c) and S1, S2, S3, S4 (“simple support type” b.c) with given Batdorf parameter, Z=1000.
Fig. 5 Buckling modes versus length of the clamped (C1) cylindrical shell (various Batdorf Z values)
FROM:
Jiabin Sun (1), Xinsheng Xu (1) and C. W. Lim (2)
(1) State Key Laboratory of Structure Analysis of Industrial Equipment and Department of Engineering Mechanics, Dalian University of Technology, Dalian, P. R. China
(2) Department of Civil and Architectural Engineering, City University of Hong Kong, Hong Kong, P. R. China
“Buckling of cylindrical shells under external pressure in a Hamiltonian system”, Journal of Theoretical and Applied Mechanics, Vol. 52, No. 3, pp. 641-653, 2014
ABSTRACT: In this article, the elastic buckling behavior of cylindrical shells under external pressure is studied by using a symplectic method. Based on Donnell’s shell theory, the governing equations which are expressed in stress function and radial displacement are re-arranged into the Hamiltonian canonical equations. The critical loads and buckling modes are reduced to solving for symplectic eigenvalues and eigenvectors. The buckling solutions are mainly grouped into four categories according to the natures of the buckling modes. The effects of geometrical parameters and boundary conditions on the buckling loads and modes are examined in detail.
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