Abstract
Conical shells under the mechanical and thermal loads are considered in this chapter. The basic governing equations of the shell including the nonlinear strain-displacement relations of Sanders assumption, the constitutive law, the nonlinear equilibrium equations, and the linear stability equations are derived employing the variational principle. The stability of the shell is considered and the buckling loads associated with the mechanical and thermal forces are derived. In case of thermal loading, the material temperature dependency is considered and the results are compared with the case where temperature dependency of the material properties are ignored. Effect of the piezo-control on stability of conical shells under thermal loading concludes the chapter.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Brush, D. O., & Almroth, B. O. (1975). Buckling of bars, plates, and shells. New York: McGraw-Hill.
Eslami, M. R. (2010). Thermo-mechanical buckling of composite plates and shells. Tehran: Amirkabir University Press.
Seide, P. (1956). Axisymmetric buckling of circular cones under axial compression. Journal of Applied Mechanics, 23, 625–628.
Seide, P. (1961). Buckling of circular cones under axial compression. Journal of Applied Mechanics, 28, 315–326.
Singer, J. (1961). Buckling of circular conical shells under axisymmetrical external pressure. Journal of Mechanical Engineering Science, 3, 330–339.
Baruch, M., & Singer, J. (1965). General instability of stiffened conical shells under hydrostatic pressure. Aero. Q., 26, 187–204.
Baruch, M., Harari, O., & Singer, J. (1967). Influence of in-plane boundary conditions on the stability of conical shells under hyrostatic pressure. Israel Journal of Technology, 5(1–2), 12–24.
Baruch, M., Harari, O., & Singer, J. (1970). Low buckling loads of axially compressed conical shells. Journal of Applied Mechanics, 37, 384–392.
Singer, J. (1962). Buckling of Orthotropic and Stiffened Conical Shells, NASA TN D-1510 (pp. 463–479).
Singer, J. (1963). Donnell-type equations for bending and buckling of orthotropic conical shells. Journal of Applied Mechanics, 30, 303–305.
Weigarten, V. I., & Seide, P. (1965a). Elastic stability of thin walled cylindrical and conical shells under combined external pressure and axial compression. AIAA Journal, 3, 913–920.
Weigarten, V. I., & Seide, P. (1965b). Elastic stability of thin walled cylindrical and conical shells under combined internal pressure and axial compression. AIAA Journal, 3, 1118–1125.
Eslami, M. R., & Rafeeyan, M. (1996). Thermal and mechanical buckling of conical shells. In Proceedings of the 8th International Conference of Pressure Vessel Technology, Montreal, Canada.
Pandey, M. D., & Sherboune, A. N. (1991). Imperfection sensitivity of optimized laminated composite shells: a physical approach. International Journal of Solids and Structures, 27(12), 1575–1595.
Palassopoulos, G. V. (1993). New approach to buckling of imperfection sensitive structures. Journal of Engineering Mechanics, 119(4), 850–869.
Kasagi, A., & Sridharan, S. (1995). Imperfection sensitivity of layered composite cylinders. Journal of Engineering Mechanics, 121(7), 810–818.
Naj, R., Sabzikar, M., & Eslami, M. R. (2008). Thermal and mechanical instability of functionally graded truncated conical shells. Thin-Walled Structures, 46(1), 65–78.
Singer, J. (1965). Buckling of circular conical shells under uniform axial compression. AIAA Journal, 3(5), 985–987.
Singer, J. (1962). The effect of axial constraint on the instability of thin conical shells under external pressure. Journal of Applied Mechanics, 29(1), 212–214.
Lu, S. Y., & Chang, L. K. (1967). Thermal buckling of conical shells. AIAA Journal, 5(10), 1877–1882.
Chang, L. K., & Lu, S. Y. (1968). Nonlinear thermal elastic buckling of conical shells. Nuclear Engineering and Design, 7(2), 159–169.
Tani, J. (1978). Influence of axisymmetric initial deflections on the thermal buckling of truncated conical shells. Nuclear Engineering and Design, 48(2–3), 393–403.
Tani, J. (1984). Buckling of truncated conical shells under combined pressure and heating. Journal of Thermal Stresses, 7(3–4), 307–316.
Tani, J. (1985). Buckling of truncated conical shells under combined axial load, pressure, and heating. Journal of Applied Mechanics, 52(2), 402–708.
Wu, C. P., & Chiu, S. J. (2001). Thermoelastic buckling of laminated composite conical shells. Journal of Thermal Stresses, 24(9), 881–901.
Patel, B. P., Shukla, K. K., & Nath, Y. (2005). Thermal postbuckling analysis of laminated cross-ply truncated circular conical shells. Composite Structures, 71(1), 101–114.
Patel, B. P., Shukla, K. K., & Nath, Y. (2006). Nonlinear thermoelastic stability characteristics of cross-ply laminated oval cylindrical/conical shells. Finite Elements in Analysis and Design, 42(12), 1061–1070.
Roh, J. H., Woo, J. H., & Lee, I. (2009). Thermal post-buckling and vibration analysis of composite conical shell structures using layerwise theory. Journal of Thermal Stresses, 32(1–2), 41–64.
Singh, B. N., & Babu, J. B. (2009). Thermal buckling of laminated composite conical shell panel with and without piezoelectric layer with random material properties. International Journal of Crashworthiness, 14(1), 73–81.
Singh, B. N., & Babu, J. B. (2009). Thermal buckling of laminated conical shells embedded with and without piezoelectric layer. Journal of Reinforced Plastics and Composites, 28(7), 731–812.
Bhangale, R., Ganesan, N., & Padmanabhan, C.h. (2006). Linear thermoelastic buckling and free vibration behavior of functionally graded truncated conical shells. J Sound and Vibration, 292(1–2), 341–371.
Sofiyev, A. H. (2007). Thermoelastic stability of functionally graded truncated conical shells. Composite Structures, 77(1), 56–65.
Sofiyev, A. H. (2011). Thermal buckling of FGM shells resting on a two-parameter elastic foundation. Thin-Walled Structure, 49(10), 1304–11.
Torabi, J., Kiani, Y., & Eslami, M. R. (2013). Linear thermal buckling analysis of truncated hybrid FGM conical shells. Composites Part B: Engineering, 50(1), 265–272.
Akbari, M., Kiani, Y., Aghdam, M. M., & Eslami, M. R. (2014). Free vibration of FGM Lévy conical panels. Composite Structures, 116, 732746. doi.org/10.1016/j.compstruct.2014.05.052.
Akbari, M., Kiani, Y., & Eslami, M. R. (2015). Thermal Buckling of temperature dependent FGM conical shells with arbitrary edge supports. Acta Mechanica, 226, 897915. doi:10.1007/s00707-014-1168-3.
Jabareen, M., & Sheinman, I. (2006). Postbuckling analysis of geometrically imperfect conical shells. Journal of Engineering Mechanics, 132(12), 1326–1334.
Jabareen, M., & Sheinman, I. (2009). Stability of imperfect stiffened conical shells. International Journal of Solids and Structures, 46(10), 2111–2125.
Sofiyev, A. H., Kuruoghlu, N., & Turkmen, M. (2009). Buckling of FGM hybrid truncated conical shells subjected to hydrostatic pressure. Thin-Walled Structures, 47, 61–72.
Sofiyev, A. H. (2009). The vibration and stability behavior of freely supported FGM conical shells subjected to external pressure. Composite Structures, 89, 356–366.
Sofiyev, A. H. (2010). The buckling of FGM truncated conical shells subjected to combined axial tension and hydrostatic pressure. Composite Structures, 92, 488–498.
Sofiyev, A. H. (2010). Buckling analysis of FGM circular shells under combined loads and resting on the Pasternak type elastic foundation. Mechanics Research Communications, 37, 539–544.
Bich, D., Phoung, N., & Tung, H. (2012). Buckling of functionally graded conical panels under mechanical loads. Composite Structures, 94, 1379–84.
Sofiyev, A. H. (2011). Influence of the initial imperfection on the non-linear buckling response of FGM truncated conical shells. International Journal of Mechanical Sciences, 53, 753–762.
Sabzikar Boroujerdy, M., & Eslami, M. R. (2015). Unsymmetrical buckling of piezo-FGM shallow clamped spherical shells under thermal loading. Journal of Thermal Stresses, 38(11), 1290–1307.
Wu, L., Jiang, Z., & Liu, J. (2005). Thermoelastic stability of functionally graded cylindrical shells. Composite Structures, 70, 60–68.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Eslami, M.R. (2018). Buckling of Conical Shells. In: Buckling and Postbuckling of Beams, Plates, and Shells. Structural Integrity, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-62368-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-62368-9_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-62367-2
Online ISBN: 978-3-319-62368-9
eBook Packages: EngineeringEngineering (R0)