Quasi-bifurcation and Imperfection-sensitivity of Cylindrical ‎Shells under Pressures due to an Explosion

Document Type : Research Paper


1 Structures Department, FCEFyN, Universidad Nacional de Córdoba, Argentina

2 Institute for Advanced Studies in Engineering and Technology (IDIT), CONICET and Universidad Nacional de Córdoba, Argentina


The static and dynamic behavior of a horizontal cylindrical shell (as used to store fuels in tanks) is investigated in this work by means of computational modeling. Under a distributed pressure commonly used to model effects due to explosions, the geometrically nonlinear behavior is explored to identify bifurcation and limit points along the static equilibrium path, and the associated displacements. Critical load reductions due to imperfections are found in the order of 25%. The dynamic analysis is next presented to identify the possibility of reaching a quasi-bifurcation. It is found that the first peak in the transient response at which the displacement reaches the same value as in the limit static case occurs for a load which is about 3.5 times the static bifurcation load. The velocity is zero at this state and is identified as a quasi-bifurcation, at which the shell is expected to display a static instability. Imperfection-sensitivity of the quasi-bifurcation load is found to be of the same order as the static one. This is the first quasi-bifurcation study of a shell to identify dynamic buckling due to a nearby explosion.


Main Subjects

[1]   Budiansky B., Roth R.S., Axisymmetric dynamic buckling of clamped shallow spherical shells, Collected papers on Stability of Shell Structures, NASA TN-1510, 1962.
[2]   Kleiber M., Kotula W., Saran M., Numerical analysis of dynamic quasi-bifurcation, Engineering Computations, 4, 1987, 48-52.
[3]   Lee L.H.N., On dynamic stability and quasi-bifurcation, International Journal of Nonlinear Mechanics, 16(1), 1981, 79-87.
[4]   Lee L.H.N., Bifurcation and uniqueness in dynamics of elastic-plastic continua, International Journal of Engineering Science, 13, 1975, 69-76.
[5]   Lee L.H.N., Quasi-bifurcations in dynamics of elasto-plastic continua, Journal of Applied Mechanics, 44(3), 1977, 413-418.
[6]   Lee L.H.N., Dynamic buckling of an inelastic column, International Journal of Solids and Structures, 17, 1981, 271-279.
[7]   Lee L.H.N., Ettestad K.L., Dynamic buckling of an ice strip by axial impact, International Journal of Impact Engineering, 1(4), 1983, 343-356.
[8]   Lee L.H.N., Ariman T., Chen C.C., Elastic-plastic buckling of buried pipelines by seismic excitation, Soil Dynamics and Earthquake Engineering, 3(4), 1984, 168-173.
[9]   Kratzig W., Eller C., Numerical algorithms for nonlinear unstable dynamic shell responses, Computers and Structures, 44(1/2), 1992, 263-271.
[10] Kratzig W., Li L.Y., On rigorous stability conditions for dynamic quasi-bifurcations, International Journal of Solids and Structures, 29(1), 1992, 97-104.
[11] Burmeister A., Ramm E., Dynamic stability analysis of shell structures, In: W. B. Kratzig, E. Oñate (eds.): Computational Mechanics of Nonlinear Response of Shells, Springer, Berlin, 1990, 152-163.
[12] Simitses G., Dynamic stability of suddenly loaded structures, Springer-Verlag, New York, 1990.
[13] Simitses G., On the dynamic buckling of shallow spherical caps, Journal of Applied Mechanics, 41(1), 1974, 299-300.
[14] Simitses G., Suddenly loaded structural configurations, ASCE Journal of Engineering Mechanics, 110(9), 1984, 1320-1334.
[15] Doyle J.F., Nonlinear Analysis of Thin-Walled Structures: Statics, dynamics and stability, Springer-Verlag, New York, 2001.
[16] Dinkler D., Kroplin B., Stability of dynamically loaded structures, In: W. B. Kratzig, E. Oñate (eds.): Computational Mechanics of Nonlinear Response of Shells, Springer, Berlin, 1990, 183-192.
[17] Dinkler D., Kroplin B., Perturbation sensitivity of dynamically loaded structures, in SN Atluri and G Yagawa (eds.): Computational Mechanics ’88, Springer, Berlin, 1 (24), 1988, 1-4.
[18] Lepik U., Bifurcation analysis of elastic-plastic cylindrical shells, International Journal of Nonlinear Mechanics, 34, 1999, 299-311.
[19] Ameijeiras M.P., Godoy L.A., On dynamic quasi-bifurcation of simple shell-like systems under impulsive loads, International Journal of Natural Disasters, Accidents and Civil Infrastructure, 18, 2018, 41-54.
[20] Burgos C.A., Jaca R.C., Godoy L.A., Post-buckling behavior of fluid-storage steel horizontal tanks, International Journal of Pressure Vessels and Piping, 162, 2018, 46-56.
[21] Duong D.H., Hanus J.L., Bouazaoui L., Pennetier O., Moriceau J., Prod’homme G., Reimeringer M., Response of a tank under blast loading – Part I: Experimental characterization, European Journal of Environmental and Civil Eng., 16(9), 2012, 1023-1041
[22] Weggel D., Whelan M.J., Rigid tank testing summary and procedures for estimating blast overpressure distribution on a cylindrical tank surface, ISSERT Report, University of North Carolina at Charlotte, NC, USA, 2013. 
[23] Putelat T., Triantafyllidis N., Dynamic stability of externally pressurized elastic rings subjected to high rates of loading, International Journal of Solids and Structures, 51, 2014, 1-12.
[24] Ameijeiras M.P., Godoy L.A., Weggel D., Whelan M.J., Incidencia del tiempo de arribo de onda en la respuesta de tanques sometidos a explosiones externas, Mecánica Computacional, 33, 2014, 931-942 (in Spanish).
[25] ABAQUS, Simulia Unified FEA, Dassault Systems, Johnston, RI, USA, 2016.
[26] Maraveas C., Balokas G.A., Tsavdaridis K. D., Numerical evaluation on shell buckling of empty thin-walled steel tanks under wind load according to current American and European design codes, Thin-Walled Structures, 95, 2015, 152-160.
[27] API 650, Welded steel tanks for oil storage, American Petroleum Institute, Washington, DC, USA, 2010.
[28] Eurocode 3. Design of steel structures – Part 1-6, strength and stability of shell structures. European Standard EN 1993-1-6, 2007.
[29] Koiter W.T., The stability of elastic equilibrium, Ph.D. Thesis, Delft, The Netherlands,1945.
[30] Rotter J.M., Schmidt H., Buckling of Steel Shells: European Design Recommendations, 5th edition, European Convention for Constructional Steel Work (ECCS), Mem Martins, Lisbon, Portugal, 2008.
[31] Bazzucchi F., Manuello A., Carpinteri A., Interaction between snap-through and Eulerian instability in shallow structures, International Journal of Non-linear Mechanics, 88, 2017, 11-20.
[32] Bazzucchi F., Manuello A., Carpinteri A., Instability load evaluation of shallow imperfection-sensitive structures by form and interaction parameters, European Journal of Mechanics - A/Solids, 66, 2017, 201-211.
[33] Ameijeiras M.P., Godoy L.A., Simplified analytical approach to evaluate the nonlinear dynamics of elastic cylindrical shells under lateral blast loads, Latin American Journal of Solids and Structures, 13(5), 2016, 1281-1298.
[34] Hindmarsh A.C., Brown P.N., Grant K.E., Lee S.L., Serban R., Shumaker D.E., Woodward C.S. SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers, ACM Transactions on Mathematical Software, 31(3), 2005, 363-396.
[35] Virella J.C., Godoy L.A., Suárez L.E., Dynamic buckling of anchored steel tanks subjected to horizontal earthquake excitation, Journal of Constructional Steel Research, 62(6), 2006, 521-531.