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Buckling Behavior under Radial Loading of Orthotropic Oval Cylindrical Shells with Parabolically Varying Thickness

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Mousa Khalifa at South Vally University, Luxor , Qena , Egypt
Mousa Khalifa
  • South Vally University, Luxor , Qena , Egypt
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Abstract

In this paper, the framework of the Flügge's shell theory, the transfer matrix approach and the Romberg integration method has been employed to investigate the buckling analysis of radial loaded oval cylindrical shell with parabolically varying thickness along of its circumference. Trigonometric functions are used to form the modal displacements of the shell and Fourier's approach is used to separate the variables. The mathematical analysis is formulated to overcome the difficulties related to mode coupling of variable curvature and thickness of the shell. Using the transfer matrix of the shell, the buckling equations of the shell are reduced to eight first-order differential equations in the circumferential coordinate and rewritten in a matrix form and solved numerically. The proposed model is adopted to get the critical buckling loads and the corresponding buckling deformations for the symmetrical and antisymmetrical modes of buckling. The influences of the shell geometry, orthotropic parameters, ovality parameter, and thickness ratio on the buckling parameters and the bending deformations are presented for different type-modes of buckling.
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Buckling Behavior under Radial Loading of Orthotropic
Oval Cylindrical Shells with Parabolically Varying
Thickness
Mousa Khalifa Ahmeda
a Department of Mathematics, Faculty of science at Qena, South Valley University, Egypt. E-
mail:
Accepted author version posted online: 18 Nov 2014.
To cite this article: Mousa Khalifa Ahmed (2014): Buckling Behavior under Radial Loading of Orthotropic Oval
Cylindrical Shells with Parabolically Varying Thickness, Mechanics of Advanced Materials and Structures, DOI:
10.1080/15376494.2014.949928
To link to this article: http://dx.doi.org/10.1080/15376494.2014.949928
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1
Buckling Behavior under Radial Loading of Orthotropic Oval Cylindrical Shells with
Parabolically Varying Thickness
Mousa Khalifa Ahmed
Department of Mathematics, Faculty of science at Qena, South Valley University, Egypt.
E-mail: mossa@dr.com
ABSTRACT
In this paper, the framework of the Flügge’s shell theory, the transfer matrix approach and the
Romberg integration method has been employed to investigate the buckling analysis of radial
loaded oval cylindrical shell with parabolically varying thickness along of its circumference.
Trigonometric functions are used to form the modal displacements of the shell and Fourier’s
approach is used to separate the variables. The mathematical analysis is formulated to overcome the
difficulties related to mode coupling of variable curvature and thickness of the shell. Using the
transfer matrix of the shell, the buckling equations of the shell are reduced to eight first-order
differential equations in the circumferential coordinate and rewritten in a matrix form and solved
numerically. The proposed model is adopted to get the critical buckling loads and the corresponding
buckling deformations for the symmetrical and antisymmetrical modes of buckling. The influences
of the shell geometry, orthotropic parameters, ovality parameter, and thickness ratio on the buckling
parameters and the bending deformations are presented for different type-modes of buckling.
Downloaded by [King Khalid University] at 23:56 10 December 2014
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