Period: 2003 - 2008 (completed)


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.

Relevant Publications:

In Referred Journals

  • 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

In Conference Proceedings

  • Karamanos, S. A., 'Stability of Straight and Bent Tubes Under In-Plane Bending.', Fourth International Colloquium on Computation of Shell & Spatial Structures, paper No. 251, Chania, Crete, Greece, June 2000.
  • Houliara, S. and Karamanos, S. A., 'Bending Instabilities of Pressurized Long Elastic Cylindrical Shells', International Conference on Computational and Experimental Engineering & Sciences, ICCES 2003, Corfu, Greece, July 2003.
  • Houliara, S., and Karamanos, S. A., "Buckling of Thin-Walled Steel Cylinders under Bending Loads.", Fifth International Colloquium on Computation of Shell & Spatial Structures, Salzburg, Austria, June 2005.
  • Houliara, S. and Karamanos, S. A., "Bending Buckling of Long Elastic Anisotropic Cylindrical Shells", ASME Congress of Applied Mechanics and Materials, MCMAT, Austin, Texas, June 2007 (abstract only).
  • Houliara, S. and Karamanos, S. A., "Buckling of Pressurized Long Elastic Anisotropic Cylindrical Shells", 8th HSTAM Congress on Mechanics, Patras, Greece, July 2007.
  • Houliara, S. and Karamanos, S. A., "Hypo-elastic and Hyper-elastic Models for the Stability Analysis of Anisotropic Cylindrical Shells", 6th GRACM International Congress on Computational Mechanics, Thessaloniki, Greece, June 2008.


pic 1

Figure 1. Pre-buckling and post-buckling shapes of a cylinder cross-section (no pressure f =0, initially straight Km =0, r/t=120)


pic 2

Figure 2. Pre-buckling and post-buckling shapes for zero pressure f=0 and critical point at θ= π/6, initial curvature Km=-1.374, and r/t=120.


pic 3
Figure 3. Buckling modes for a thin-walled transversly-isotropic cylinder r/t=720, for high values of anisotropy parameter S.


pic 4
Figure 4. Imperfection sensitivity of a transversely-isotropic cylinder; maximum moment on the m - k path.

Spyros A. Karamanos, PhD

Department of Mechanical Engineering | University of Thessaly | Pedion Areos, Volos 38334, Greece
Phone: +30 - 24210 74086, 74360 | Fax : +30 - 24210 74360 | Email: This email address is being protected from spambots. You need JavaScript enabled to view it.

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