An Analytical Procedure for Buckling Load Determination of an Axisymmetric Cylinder with Non-Uniform Thickness Using Shear Deformation Theory

Document Type : Research Article

Authors

Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology, Shahrood, Iran

Abstract

In this article, the buckling load of an axisymmetric cylindrical shell with a variable
thickness is determined analytically by using the perturbation method. The loading is axial and the
material properties are defined by the Hooke’s law. The displacement field is predicted by using the
first order shear deformation theory and the nonlinear von-Karman relations are used for the kinematic
description of the shell. The stability equations, which are the system of nonlinear differential equations
with variable coefficients, are derived by the virtual work principle and are solved using the perturbation
technique. Also, the buckling load is determined by using the finite element method and it is compared
with the analytical solution results, the classical shell theory, and other references. The effects of linear
and nonlinear shell profiles variation on the axial buckling load are investigated. Also, we studied the
effects of geometric parameters on the buckling load results. The results show that the first order shear
deformation theory is more useful for buckling load determination of thicker shells.

Highlights

[1] J. Hutchinson, Axial buckling of pressurized imperfect cylindrical shells, AIAA J, 3(8) (1965) 1461-1466.

[2] V. Weingarten, E. Morgan, P. Seide, Elastic stability of thin-walled cylindrical and conical shells under axial compression, AIAA J, 3(3) (1965) 500-505.

[3] Z. Malik, J. Morton, C. Ruiz, An experimental investigation into the buckling of cylindrical shells of variable-wall thickness under radial external pressure, Experimental Mechanics, 19(3) (1979) 87-92.

[4] F. Mahboubi Nasrekani, H. Eipakchi, Elastic buckling of axisymmetric cylindrical shells under axial load using first order shear deformation theory, ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 92(11.12) (2012) 937-944.

[5] W. Koiter, I. Elishakoff, Y. Li, J. Starnes, Buckling of an axially compressed cylindrical shell of variable thickness, International Journal of Solids and Structures, 31(6) (1994) 797-805.

[6] Y. Li, I. Elishakoff, J. Starnes, Axial buckling of composite cylindrical shells with periodic thickness variation, Computers & structures, 56(1) (1995) 65-74.

[7] I. Andrianov, B. Ismagulov, M. Matyash, Buckling of cylindrical shells of variable thickness, loaded by external uniform pressure, Tech. Mech, 20(4) (2000) 349-354.

[8] G. Gusic, A. Combescure, J. Jullien, The influence of circumferential thickness variations on the buckling of cylindrical shells under external pressure, Computers & Structures, 74(4) (2000) 461-477.

[9] A.H. Sofiyev, H. Erdem, The stability of non-homogeneous elastic cylindrical thin shells with variable thickness under a dynamic external pressure, Turkish Journal of Engineering and Environmental Sciences, 26(2) (2002) 155-166.

[10] S. Filippov, D. Ivanov, N. Naumova, Free vibrations and buckling of a thin cylindrical shell of variable thickness with curve linear edge, Technische Mechanik, 25(1) (2005) 1-8.

[11] S. Aghajari, K. Abedi, H. Showkati, Buckling and post-buckling behavior of thin-walled cylindrical steel shells with varying thickness subjected to uniform external pressure, Thin-walled structures, 44(8) (2006) 904-909.

[12] N.T.H. Luong, T.S.S. Hoach, Stability of cylindrical panel with variable thickness, Vietnam Journal of Mechanics, 28(1) (2006) 56-65.

[13] H.L.T. Nguyen, I. Elishakoff, V.T. Nguyen, Buckling under the external pressure of cylindrical shells with variable thickness, International Journal of Solids and Structures, 46(24) (2009) 4163-4168.

[14] Y. Fakhim, H. Showkati, K. Abedi, Experimental study on the buckling and post-buckling behavior of thin-walled cylindrical shells with varying thickness under hydrostatic pressure, in: Proceedings of the international association for shell and spatial structures (IASS) symposium, 2009.

[15] L. Chen, J.M. Rotter, C. Doerich, Buckling of cylindrical shells with stepwise variable wall thickness under uniform external pressure, Engineering Structures, 33(12) (2011) 3570-3578.

[16] Z. Chen, L. Yang, G. Cao, W. Guo, Buckling of the axially compressed cylindrical shells with arbitrary axisymmetric thickness variation, Thin-Walled Structures, 60 (2012) 38-45.

[17] M. Shariyat, D. Asgari, Nonlinear thermal buckling and postbuckling analyses of imperfect variable thickness temperature-dependent bidirectional functionally graded cylindrical shells, International Journal of Pressure Vessels and Piping, 111 (2013) 310-320.

[18] R.A. Alashti, S.A. Ahmadi, Buckling of imperfect thick cylindrical shells and curved panels with different boundary conditions under external pressure, Journal of Theoretical and Applied Mechanics, 52 (2014) 25-36.

[19] H.-G. Fan, Z.-P. Chen, W.-Z. Feng, F. Zhou, G.-W. Cao, Dynamic buckling of cylindrical shells with arbitrary axisymmetric thickness variation under time dependent external pressure, International Journal of Structural Stability and Dynamics, 15(03) (2015) 1450053.

[20] F. Zhou, Z. Chen, H. Fan, S. Huang, Analytical study on the buckling of cylindrical shells with stepwise variable thickness subjected to uniform external pressure, Mechanics of Advanced Materials and Structures, 23(10) (2016) 1207-1215.

[21] M. Amabili, Nonlinear vibrations and stability of shells and plates, Cambridge University Press, New York, 2008.

[22] X. Xu, J. Ma, C.W. Lim, H. Chu, Dynamic local and global buckling of cylindrical shells under axial impact, Engineering Structures, 31(5) (2009) 1132-1140.

[23] A.H. Nayfeh, Introduction to perturbation techniques, John Wiley & Sons, New York, 1981.

[24] S. Timoshenko, Theory of elastic stability, 2 ed., McGraw-Hill, New York, 1963.

Keywords

References

[1] J. Hutchinson, Axial buckling of pressurized imperfect cylindrical shells, AIAA J, 3(8) (1965) 1461-1466.
[2] V. Weingarten, E. Morgan, P. Seide, Elastic stability of thin-walled cylindrical and conical shells under axial compression, AIAA J, 3(3) (1965) 500-505.
[3] Z. Malik, J. Morton, C. Ruiz, An experimental investigation into the buckling of cylindrical shells of variable-wall thickness under radial external pressure, Experimental Mechanics, 19(3) (1979) 87-92.
[4] F. Mahboubi Nasrekani, H. Eipakchi, Elastic buckling of axisymmetric cylindrical shells under axial load using first order shear deformation theory, ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 92(11.12) (2012) 937-944.
[5] W. Koiter, I. Elishakoff, Y. Li, J. Starnes, Buckling of an axially compressed cylindrical shell of variable thickness, International Journal of Solids and Structures, 31(6) (1994) 797-805.
[6] Y. Li, I. Elishakoff, J. Starnes, Axial buckling of composite cylindrical shells with periodic thickness variation, Computers & structures, 56(1) (1995) 65-74.
[7] I. Andrianov, B. Ismagulov, M. Matyash, Buckling of cylindrical shells of variable thickness, loaded by external uniform pressure, Tech. Mech, 20(4) (2000) 349-354.
[8] G. Gusic, A. Combescure, J. Jullien, The influence of circumferential thickness variations on the buckling of cylindrical shells under external pressure, Computers & Structures, 74(4) (2000) 461-477.
[9] A.H. Sofiyev, H. Erdem, The stability of non-homogeneous elastic cylindrical thin shells with variable thickness under a dynamic external pressure, Turkish Journal of Engineering and Environmental Sciences, 26(2) (2002) 155-166.
[10] S. Filippov, D. Ivanov, N. Naumova, Free vibrations and buckling of a thin cylindrical shell of variable thickness with curve linear edge, Technische Mechanik, 25(1) (2005) 1-8.
[11] S. Aghajari, K. Abedi, H. Showkati, Buckling and post-buckling behavior of thin-walled cylindrical steel shells with varying thickness subjected to uniform external pressure, Thin-walled structures, 44(8) (2006) 904-909.
[12] N.T.H. Luong, T.S.S. Hoach, Stability of cylindrical panel with variable thickness, Vietnam Journal of Mechanics, 28(1) (2006) 56-65.
[13] H.L.T. Nguyen, I. Elishakoff, V.T. Nguyen, Buckling under the external pressure of cylindrical shells with variable thickness, International Journal of Solids and Structures, 46(24) (2009) 4163-4168.
[14] Y. Fakhim, H. Showkati, K. Abedi, Experimental study on the buckling and post-buckling behavior of thin-walled cylindrical shells with varying thickness under hydrostatic pressure, in: Proceedings of the international association for shell and spatial structures (IASS) symposium, 2009.
[15] L. Chen, J.M. Rotter, C. Doerich, Buckling of cylindrical shells with stepwise variable wall thickness under uniform external pressure, Engineering Structures, 33(12) (2011) 3570-3578.
[16] Z. Chen, L. Yang, G. Cao, W. Guo, Buckling of the axially compressed cylindrical shells with arbitrary axisymmetric thickness variation, Thin-Walled Structures, 60 (2012) 38-45.
[17] M. Shariyat, D. Asgari, Nonlinear thermal buckling and postbuckling analyses of imperfect variable thickness temperature-dependent bidirectional functionally graded cylindrical shells, International Journal of Pressure Vessels and Piping, 111 (2013) 310-320.
[18] R.A. Alashti, S.A. Ahmadi, Buckling of imperfect thick cylindrical shells and curved panels with different boundary conditions under external pressure, Journal of Theoretical and Applied Mechanics, 52 (2014) 25-36.
[19] H.-G. Fan, Z.-P. Chen, W.-Z. Feng, F. Zhou, G.-W. Cao, Dynamic buckling of cylindrical shells with arbitrary axisymmetric thickness variation under time dependent external pressure, International Journal of Structural Stability and Dynamics, 15(03) (2015) 1450053.
[20] F. Zhou, Z. Chen, H. Fan, S. Huang, Analytical study on the buckling of cylindrical shells with stepwise variable thickness subjected to uniform external pressure, Mechanics of Advanced Materials and Structures, 23(10) (2016) 1207-1215.
[21] M. Amabili, Nonlinear vibrations and stability of shells and plates, Cambridge University Press, New York, 2008.
[22] X. Xu, J. Ma, C.W. Lim, H. Chu, Dynamic local and global buckling of cylindrical shells under axial impact, Engineering Structures, 31(5) (2009) 1132-1140.
[23] A.H. Nayfeh, Introduction to perturbation techniques, John Wiley & Sons, New York, 1981.
[24] S. Timoshenko, Theory of elastic stability, 2 ed., McGraw-Hill, New York, 1963.
AUT Journal of Mechanical Engineering
Volume 1, Issue 2
December 2017
Pages 211-218

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