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Buckling of oval cylindrical shell in bending

From: the PhD thesis of S. Houliara, "Computational techniques in structural stability of thin-walled cylindrical shells", 2003-2008 (completed), Faculty Advisor: Spyros A. Karamanos, Associate Professor, Department of Mechanical Engineering, University of Thessaly, Greece

Summary of Thesis: The research examines instabilities of long pressurized thin elastic tubes. The material is isotropic or transversely-isotropic, and it is modeled through a hypo-elastic constitutive equation. Both initially straight and initially bent tubes are analyzed under in-plane bending and pressure. Tube response, a combination of ovalization instability and bifurcation instability (buckling), is investigated using a nonlinear finite element technique, which employs polynomial functions in the longitudinal tube direction and trigonometric functions to describe cross-sectional deformation. It is demonstrated that the interaction between the two instability modes depends on the value and the sign of the initial tube curvature.

The work emphasizes on bifurcation instability. It is shown that buckling may occur prior to or beyond the ovalization limit point, depending on the value of the initial curvature. Using the nonlinear finite element formulation, the location of bifurcation on the primary path is detected, post-buckling equilibrium paths are traced, and the corresponding wavelengths of the buckled configurations are calculated for a range of initial curvature values and in terms of pressure. Results over a wide range of initial curvature values are presented. The effects of anisotropy on the buckling moment, the buckling mode and the post-buckling response are also examined.

Finally, an analytical approach is also employed to estimate the bending moment causing bifurcation instability. The approach is based on the DMV shell equations considering pre-buckling solutions from simplified ring analysis. The efficiency and accuracy of the analytical method with respect to the nonlinear finite element formulation are examined.

See the following publications:
Karamanos, S. A., 'Bending Instabilities of Elastic Tubes.', International Journal of Solids & Structures, Vol. 39, No. 8, pp. 2059-2085, April 2002.
Houliara, S. and Karamanos, S. A., 'Buckling and Post-Buckling of Pressurized Thin-Walled Elastic Tubes Under In-Plane Bending.', International Journal of Nonlinear Mechanics, Vol. 41, No. 4, pp. 491-511, May 2006.
Houliara, S. and Karamanos, S. A., "Stability of Long Transversely-Isotropic Elastic Cylinders Under Bending.", International Journal of Solids and Structures, Vol. 47, No. 1, pp. 10-24, January 2010

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