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Structural Engineering and Mechanics Volume 16, Number 6, December 2003 , pages 731-748 DOI: https://doi.org/10.12989/sem.2003.16.6.731 |
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Closed form solution for displacements of thick cylinders with varying thickness subjected to non-uniform internal pressure |
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H.R. Eipakchi, G.H. Rahimi and S. Esmaeilzadeh Khadem
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| Abstract | ||
| In this paper a thick cylindrical shell with varying thickness which is subjected to static non-uniform internal pressure is analyzed. At first, equilibrium equations of the shell have been derived by the energy principle and by considering the first order theory of Mirsky-Herrmann which includes transverse shear deformation. Then the governing equations which are, a system of differential equations with varying coefficients have been solved analytically with the boundary layer technique of the perturbation theory. In spite of complexity of modeling the conditions near the boundaries, the method of this paper is very capable of providing a closed form solution even near the boundaries. Displacement predictions are in a good agreement with the calculated finite elements and other analytical results. The convergence of solution is very fast and the amount of calculations is less than the Frobenius method. | ||
| Key Words | ||
| thick cylindrical shell; varying thickness; perturbation theory; finite elements method. | ||
| Address | ||
| Department of Mechanical Engineering, Tarbiat Modarres University, P. O. Box 14115-143 Tehran, I.R. Iran | ||