Analytical buckling load formulas for cylindrical shell structures with variable thickness under non-uniform external pressure

Abstract

The novel contribution of this paper is to develop a quadratic perturbation method to derive general analytical buckling load formulas for cylindrical shell structures with varying wall thickness under non-uniform lateral pressure loads for the first time. Arbitrary thickness and lateral pressure loads are skillfully described and governing differential equations are derived. A quadratic perturbation method is developed to derive buckling load formulas, which establishes the relation among buckling loads, thickness, and load functions. The presented formulas are adequately validated by comparing with recent results for variable wall thickness or non-uniform external pressure, and exhibit a great advantage in determining buckling loads. For the purpose of engineering application, buckling of a cylinder with linear thickness under linear liquid pressure and wind load is deeply studied by the presented formulas. This study can provide a highly efficient method for buckling load computation, and a guide to design the thickness of the shell under non-uniform lateral loads.

Keywords

Buckling cylindrical shells quadratic perturbation method variable thickness non-uniform external pressure

Get full access to this article

View all access options for this article.

References

Gusic

Combescure

Jullien

JF.

The influence of circumferential thickness variations on the buckling of cylindrical shells under lateral pressure. Comput Struct 2000; 74: 461–477.

Combescure

Gusic

Nonlinear buckling of cylinders under lateral pressure with nonaxisymmetric thickness imperfections using the COMI axisymmetric shell element. Int J Solids Struct 2001; 38: 6207–6226.

Aghajari

Abedi

Showkati

Buckling and post-buckling behavior of thin-walled cylindrical steel shells with varying thickness subjected to uniform external pressure. Thin-Walled Struct 2006; 44: 904–909.

Nguyen

HLT

Elishakoff

Nguyen

VT.

Buckling under the external pressure of cylindrical shells with variable thickness. Int J Solids Struct 2009; 46: 4163–4168.

Chen

Rotter

Doerich

Buckling of cylindrical shells with stepwise variable wall thickness under uniform external pressure. Eng Struct 2011; 33: 3570–3578.

Chen

Rotter

Doerich

Practical calculations for uniform external pressure buckling in cylindrical shells with stepped walls. Thin-Walled Struct 2012; 61: 162–168.

Yang

Chen

Cao

, et al. An analytical formula for elastic-plastic instability of large oil storage tanks. Int J Pres Ves Pip 2013; 101: 72–80.

Yang

Chen

, et al. Buckling of cylindrical shells with general axisymmetric thickness imperfections under external pressure. Eur J Mech A-solid 2013; 38: 90–99.

Yang

Luo

Qiu

, et al. An analytical method for the buckling analysis of cylindrical shells with non-axisymmetric thickness variations under external pressure. Thin-Walled Struct 2014; 85: 431–440.

10.

Zhou

Chen

Fan

, et al. Analytical study on the buckling of cylindrical shells with stepwise variable thickness subjected to uniform external pressure. Mech Adv Mater Struct 2016; 23: 1207–1215.

11.

Mahboubi Nasrekani

Eipakchi

. Analytical solution for buckling analysis of cylinders with varying thickness subjected to combined axial and radial loads. Int J Pres Ves Pip 2019; 172: 220–226.

12.

Fazlalipour

Showkati

Firouzsalari

SE.

Buckling behavior of cylindrical shells with stepwise wall thickness subjected to combined axial compression and external pressure. Thin-Walled Struct 2021; 167: 108195.

13.

Resinger

Greiner

. Buckling of wind loaded cylindrical shells: application to unstiffened and ring-stiffened tanks. Buckling of shells. In: Proceedings of a state-of-the-art colloquium, University Stuttgart, 6–7 May 1982, pp. 305–331. Berlin: Springer.

14.

Jerath

Ghosh

AK.

Buckling of cylindrical shells under the action of nonuniform external pressure. Comput Struct 1987; 25: 607–614.

15.

Lin

ZQ.

Non-linear buckling and postbuckling of shear deformable anisotropic laminated cylindrical shell subjected to varying external pressure loads. Compos Struct 2010; 92: 553–567.

16.

Zhao

Cao

Buckling design of large circular steel silos subject to wind pressure. Thin-Walled Struct 2013; 73: 337–349.

17.

Obodan

Lebedev

Gromov

VA.

Nonlinear behaviour and stability of thin-walled shells. Dordrecht; Heidelberg; New York; London: Springer, 2013.

18.

Azzuni

Guzey

A perturbation approach on buckling and postbuckling of circular rings under nonuniform loads. Int J Mech Sci 2018; 137: 86–95.

19.

Andrianov

. Analytical investigation of buckling of a cylindrical shell subjected to nonuniform external pressure. Math Mech Solids 2019; 24: 874–883.

20.

Wang

Yang

Zeng

, et al. Post-buckling behavior of stiffened cylindrical shell and experimental validation under non-uniform external pressure and axial compression. Thin-Walled Struct 2021; 161: 107481.

21.

Yang

Luo, Y, Qiu

Zheng

, et al. A novel analytical study on the buckling of cylindrical shells subjected to arbitrarily distributed external pressure. Eur J Mech A Solids 2022; 91: 104406.

22.

Andreev

Obodan

NI.

Stability of shells of varying thickness under arbitrary external loads. Soviet Appl Mech 1974; 10: 32–36.

23.

Baker

Graves-Morris

Padé approximants. Cambridge: Cambridge University Press, 1996.