Buckling of Thin Shells: Recent Advances and Trends

This paper provides a review of recent research advances and trends in the area of thin shell buckling. Only the more important and interesting aspects of recent research, judged from a personal view point, are discussed. In particular, the following topics are given emphasis: (a) imperfections in real structures and their influence; (b) buckling of shells under local/non-uniform loads and localized compressive stresses; and (c) the use of computer buckling analysis in the stability design of complex thin shell structures. I INTRODUCTION Thin-shell structures find wide applications in many branches of engineering. Examples include aircraft, spacecraft, cooling towers, nuclear reactors, steel silos and tanks for bulk solid and liquid storage, pressure vessels, pipelines and offshore platforms. Because of the thinness of these structures, buckling is often the controlling failure mode. It is therefore essential that their buckling behavior be properly understood so that suitable design methods can be established. This paper provides a review of recent research advances and trends in the area of thin shell buckling. The paper is not intended to be an exhaustive review of the field, nor is it possible to do so in a single paper of limited length. Instead, only the more important and interesting aspects of recent research, judged from a personal viewpoint, will be discussed. In particular, the following topics are given emphasis: (a) imperfections in real structures and their influence; (b) buckling of shells under local/non-uniform loads and localized compressive stresses; and (c) the use of computer buckling analysis in the stability design of complex thin shell structures. The author wishes to apologize in advance for any inadvertent omission of relevant publications.

[1]  R. Peek,et al.  Postbuckling behavior of unanchored steel tanks under lateral loads , 1991 .

[2]  Rakesh K. Kapania,et al.  Stability of cylindrical shells under combined wind and snow loads , 1990 .

[3]  David Bushnell,et al.  B0S0R5—program for buckling of elastic-plastic complex shells of revolution including large deflections and creep , 1976 .

[4]  J. M. Rotter,et al.  Nonsymmetric Buckling of Plate-End Pressure Vessels , 1989 .

[5]  Stelios Kyriakides,et al.  On the beam and shell modes of buckling of buried pipelines , 1990 .

[6]  Jin-Guang Teng Cone‐Cylinder Intersection under Pressure: Axisymmetric Failure , 1994 .

[7]  Vlastimil Křupka The background to a new design proposal for saddle supported vessels , 1991 .

[8]  J. Singer The Status of Experimental Buckling Investigations of Shells , 1982 .

[9]  Endre Dulácska,et al.  Buckling of Shells for Engineers , 1984 .

[10]  Viggo Tvergaard,et al.  Effect of residual stresses on plastic buckling of cylindrical shell structures , 1990 .

[11]  R. C. Tennyson,et al.  The effects of unreinforced circular cutouts on the buckling of circular cylindrical shells under axial compression. , 1968 .

[12]  J E Harding,et al.  TORSIONAL BUCKLING OF RING-STIFFENERS IN CYLINDRICAL SHELLS SUBJECTED TO EXTERNAL PRESSURE. , 1994 .

[13]  Jiro Adachi,et al.  Buckling of torispherical shells under internal pressure , 1964 .

[14]  J. Teng,et al.  Elastic Stability of Cylindrical Shells with Weld Depressions , 1989 .

[15]  Haim Abramovich,et al.  The development of shell imperfection measurement techniques , 1995 .

[16]  I. J. Ross,et al.  Closure of "Bin-Wall Failure Caused by Eccentric Discharge of Free-Flowing Grain" , 1990 .

[17]  J. Arbocz,et al.  The Imperfection Data Bank, a Mean to Obtain Realistic Buckling Loads , 1982 .

[18]  Nathan M. Newmark,et al.  The Strength of Thin Cylindrical Shells as Columns , 1975 .

[19]  V. I. Ishakov Effect of large deflections and initial imperfections on buckling of flexible shallow hyperbolic paraboloid shells , 1993 .

[20]  G. D. Galletly,et al.  INTERACTIVE BUCKLING TESTS ON CYLINDERS SUBJECTED TO EXTERNAL PRESSURE AND AXIAL COMPRESSION , 1987 .

[21]  E. V. Pittner,et al.  Design criteria for axially loaded cylindrical shells , 1970 .

[22]  Wei Zhang,et al.  Study on elephant-foot buckling of broad liquid storage tanks by nonlinear theory of shells , 1992 .

[23]  Jin-Guang Teng,et al.  Out‐of‐Plane Buckling of Restrained Thin Rings of General Open Section , 1994 .

[24]  Xiaoli Ding,et al.  A Profile Measurement System and its Application in Precise Engineering Surveying , 1991 .

[25]  J. L. Sanders,et al.  NONLINEAR THEORIES FOR THIN SHELLS , 1963 .

[26]  J. M. T. Thompson,et al.  Collapse, the buckling of structures in theory and practice : symposium, University College, London, 31 August to 3 September 1982 , 1983 .

[27]  Noriyuki Miyazaki,et al.  Bifurcation creep buckling analysis of circular cylindrical shell under axial compression , 1992 .

[28]  Srinivasan Sridharan,et al.  Localized collapse of shells of revolution using a local‐global strategy , 1992 .

[29]  Haim Abramovich,et al.  Vibration Techniques for Definition of Practical Boundary Conditions in Stiffened Shells , 1979 .

[30]  W. Guggenberger Buckling and postbuckling of imperfect cylindrical shells under external pressure , 1995 .

[31]  S. Yamada,et al.  Buckling and Post-buckling Characteristics of Pressure-Loaded Cylinders , 1993 .

[32]  Yijung Chen,et al.  Recent Advances in Dynamic Buckling Analysis of Liquid-Filled Shells , 1991 .

[33]  J. Teng Elastic buckling of cone-cylinder intersection under localized circumferential compression , 1996 .

[34]  Akira Niwa,et al.  Buckling of cylindrical liquid-storage tanks under earthquake loading , 1982 .

[35]  Walter Wunderlich,et al.  Nonlinear Behavior of externally pressurized toriconical shells - analysis and design criteria , 1987 .

[36]  Masaaki Takayanagi,et al.  Analysis of Shear Buckling of Cylindrical Shells , 1993 .

[37]  Peilin Luo,et al.  THE INFLUENCE OF PREBUCKLING DEFORMATIONS AND STRESSES ON THE BUCKLING OF SPHERICAL SHELL , 1991 .

[38]  J. G. Teng,et al.  Elastic-plastic large deflection analysis of axisymmetric shells , 1989 .

[39]  Johann Arbocz,et al.  First-order second-moment analysis of the buckling of shells with Random imperfections , 1987 .

[40]  G. Simitses,et al.  Elastic stability of circular cylindrical shells , 1984 .

[41]  J. M. Rotter,et al.  A Study of Buckling in Column-Supported Cylinders , 1992 .

[42]  P. Ansourian On the buckling analysis and design of silos and tanks , 1992 .

[43]  J. M. Rotter,et al.  Stability assessment of complex shell structures by numerical analysis , 1995 .

[44]  J. G. Teng,et al.  Buckling of rings in column-supported bins and tanks , 1989 .

[45]  Harold Crate,et al.  Buckling of thin-walled cylinder under axial compression and internal pressure , 1951 .

[46]  David Abir Thermal Buckling of Circular Cylindrical Shells Under Circumferential Temperature Gradients , 1959 .

[47]  Zenon Waszczyszyn,et al.  Buckling analysis of a cooling tower shell with measured and theoretically-modelled imperfections , 1995 .

[48]  C. R. Calladine,et al.  Plastic buckling of tubes in pure bending , 1982 .

[49]  Ernest T. Selig,et al.  Use of Continuum Buckling Theory for Evaluation of Buried Plastic Pipe Stability , 1990 .

[50]  J. Hutchinson,et al.  A survey of some buckling problems. , 1966 .

[51]  Manuel Stein,et al.  The Influence of Prebuckling Deformations and Stresses on the Buckling of Perfect Cylinders , 1964 .

[52]  M. Chiba,et al.  Buckling of circular cylindrical shells partially subjected to external liquid pressure , 1989 .

[53]  David J. O'Connor Computerised buckling analysis of shells: D. Bushnell. Martinus Nijhoff Publishers, Netherlands, August '85 423 pp. ISBN: 90-247-3099-6 Dfl 240.00 US$ 85.00. £ 60.95 , 1986 .

[54]  Steven W. Kirkpatrick,et al.  Dynamic plastic buckling of copper cylindrical shells , 1991 .

[55]  M. A. Souza,et al.  A new technique for the prediction of buckling loads from nondestructive vibration tests , 1991 .

[56]  J. M. Rotter,et al.  Elastic Buckling of Stiffened Ringbeams for Large Elevated Bins , 1985 .

[57]  J F Carney,et al.  Buckle Propagation in Submarine Pipelines , 1992 .

[58]  E. Dulacska,et al.  Design procedure for the buckling analysis of reinforced concrete shells , 1995 .

[59]  Norman Jones,et al.  Dynamic and static axial crushing of axially stiffened cylindrical shells , 1990 .

[60]  J. G. Teng,et al.  Linear bifurcation of perfect column-supported cylinders: Support modelling and boundary conditions , 1992 .

[61]  Alain Combescure,et al.  Dynamic buckling of stiffened cylindrical shells of revolution under a transient lateral pressure shock wave , 1995 .

[62]  George D. Panagiotopoulos,et al.  Stress and stability analysis of toroidal shells , 1985 .

[63]  A.M.C. Holmes,et al.  Buckling of shells with cutouts, experiment and analysis☆ , 1972 .

[64]  D. J. Gorman,et al.  An analytical and experimental investigation of the effects of large prebuckling deformations on the buckling of clamped thin-walled circular cylindrical shells subjected to axial loading and internal pressure , 1970 .

[65]  C. G. Foster,et al.  Axial load capacity of cylindrical shells with local geometric defects , 1991 .

[66]  J. Hol,et al.  Collapse of axially compressed cylindrical shells with random imperfections , 1991 .

[67]  Jin‐Guang Teng Plastic Collapse at Lap Joints in Pressurized Cylinders under Axial Load , 1994 .

[68]  A. E. Elwi,et al.  Shear behavior of large-diameter fabricated steel tubes , 1987 .

[69]  P. Ansourian,et al.  Stability of silo wall stiffened by particulate solids , 1991 .

[70]  George J. Simitses,et al.  Buckling and Postbuckling of Imperfect Cylindrical Shells: A Review , 1986 .

[71]  B. O. Almroth,et al.  Influence of stiffener eccentricity and end moment on stability of cylinders in compression. , 1966 .

[72]  C. R. Calladine,et al.  Understanding imperfection-sensitivity in the buckling of thin-walled shells , 1995 .

[73]  R. Kałuza,et al.  Experimental analysis of the influence of imposed displacements at the base of a cooling tower on its buckling stability , 1995 .

[74]  D. J. Johns On the Linear Buckling of Circular Cylindrical Shells Under Asymmetric Axial Compressive Stress Distributions , 1966, The Journal of the Royal Aeronautical Society.

[75]  Guy Lagae,et al.  Stresses in and buckling of unstiffened cylinders subjected to local axial loads , 1993 .

[76]  J. Singer Vibration techniques for definition of practical boundary conditionsin stiffened shells , 1978 .

[77]  Piping Division,et al.  Pressure vessels and piping : design technology, 1982--a decade of progress , 1982 .

[78]  S. Kyriakides,et al.  Bifurcation and localization instabilities in cylindrical shells under bending—I. Experiments , 1992 .

[79]  Nicholas J. Hoff Low Buckling Stresses of Axially Compressed Circular Cylindrical Shells of Finite Length , 1965 .

[80]  David Durban,et al.  A Method for Approximate Stability Analysis and Its Application to Circular Cylindrical Shells Under Circumferentially Varying Edge Loads , 1973 .

[81]  Yasushi Uematsu,et al.  EXPERIMENTS ON THE DEFLECTION AND BUCKLING BEHAVIOR OF RING-STIFFENED CYLINDRICAL SHELLS UNDER WIND PRESSURE , 1987 .

[82]  Wang De-yu,et al.  The impact torsional buckling of elastic cylindrical shells with arbitrary form imperfection , 1993 .

[83]  George G. Adams Elastic Wrinkling of a Tensioned Circular Plate Using von Kármán Plate Theory , 1993 .

[84]  C. R. Calladine,et al.  The Theory of Thin Shell Structures 1888–1988 , 1988 .

[85]  J. Michael Rotter,et al.  Buckling of Restrained Monosymmetric Rings , 1988 .

[86]  J. Michael Rotter,et al.  Elastic Buckling of Imperfect Cylinders Containing Granular Solids , 1990 .

[87]  Jin-Guang Teng Cone-cylinder intersection under internal pressure : nonsymmetric buckling , 1995 .

[88]  Archibald N. Sherbourne,et al.  Buckling of Cylindrical Shells Under Axial Compression , 1967 .

[89]  V. Křupka Plastic Squeeze of Circular Shell due to Saddle or Lug , 1992 .

[90]  J. M. Rotter The Design of Circular Metal Silos for Strength , 1993 .

[91]  J. M. Rotter,et al.  Buckling in Thin Elastic Cylinders on Column Supports , 1991 .

[92]  M. B. Marlowe,et al.  Stability analysis of cylinders with circular cutouts , 1973 .

[93]  J. Jullien,et al.  Creep buckling of cylindrical shells under external lateral pressure , 1995 .

[94]  J. M. Rotter,et al.  The Analysis of Steel Bins Subject to Eccentric Discharge , 1986 .

[95]  S. Kyriakides,et al.  Bifurcation and localization instabilities in cylindrical shells under bending-II. Predictions , 1992 .

[96]  R. Greiner,et al.  Effect of imperfections on wind-loaded cylindrical shells , 1995 .

[97]  J. M. Rotter,et al.  Shell Restraint to Ringbeam Buckling in Elevated Steel Silos , 1987 .

[98]  R. C. Tennyson,et al.  Buckling of circular cylindrical shells in axial compression buckling of circular cylindrical shells in axial compression. buckling of circular cylindrical shells in axial compression , 1964 .

[99]  Nicholas J. Hoff,et al.  Buckling of Axially Compressed Circular Cylindrical Shells at Stresses Smaller Than the Classical Critical Value , 1965 .

[100]  J. M. Rotter The Buckling and Plastic Collapse of Ring Stiffeners at Cone/Cylinder Junctions , 1987 .

[101]  Ralf Peek Buckling Criteria for Earthquake-Induced Overturning Stresses in Cylindrical Liquid Storage Tanks , 1989 .

[102]  Zheng-An Xu,et al.  Buckling of compound hyperbolic paraboloidal shells , 1992 .

[103]  S. M. Arnold,et al.  Creep Buckling of Cylindrical Shell Under Variable Loading , 1989 .

[104]  Dov I. Shilkrut,et al.  Bifurcation in Tension of Nonlinear Spherical Caps , 1983 .

[105]  D. C. Ma,et al.  Flow-structure vibration and sloshing--1990 , 1990 .

[106]  J. M. Rotter,et al.  Buckling of Simple Ringbeams for Bins and Tanks , 1983 .

[107]  J. M. Rotter,et al.  Plastic buckling of rings at steel silo transition junctions , 1991 .

[108]  Chen,et al.  Buckling Propagation in Marine Pipelines , 1993 .

[109]  John C. Yao,et al.  BUCKLING OF A TRUNCATED HEMISPHERE UNDER AXIAL TENSION , 1963 .

[110]  David Durban,et al.  Buckling of Cylindrical Shells Subjected to Nonuniform Axial Loads , 1977 .

[111]  Vistasp M. Karbhari,et al.  Nondestructive Load Predictions of Concrete Shell Buckling , 1989 .

[112]  F. P. J. Rimrott,et al.  Nonlinear instability of corrugated diaphragms , 1992 .

[113]  A. Von Flotow Non-linear strain-displacement relations and flexible multibody dynamics , 1989 .

[114]  J. F. Jullien,et al.  Buckling of shell structures, on land, in the sea, and in the air , 1991 .

[115]  Stelios Kyriakides,et al.  Inelastic Buckling of Tubes Under Cyclic Bending , 1987 .

[116]  Geoffrey L. Kulak,et al.  Flexural and shear behaviour of large diameter steel tubes , 1984 .

[117]  D. Vandepitte,et al.  Experimental Investigation of Buckling of Hydrostatically Loaded, Conical Shells and Practical Evaluation of the Buckling Load , 1982 .

[118]  P. L. Gould,et al.  Nonlinear analysis of shells of revolution , 1993 .

[119]  Karl Schweizerhof,et al.  Buckling of cylindrical shells containing granular solids , 1995 .

[120]  R. A. Uras,et al.  Buckling of Force-Excited Liquid-Filled Shells , 1991 .

[121]  Gwo-Tarng Ju Bifurcation and localization instabilities in plastic bending of cylindrical shells , 1991 .

[122]  Hiroshi Akiyama,et al.  BUCKLING TESTS OF STEEL CYLINDRICAL SHELLS SUBJECTED TO COMBINED BENDING AND SHEAR , 1987 .

[123]  G. Fischer Über die Berechnung der kritischen Axiallasten gelenkig gelagerter Kreiszylinderschalen mit Hilfe des Mehrstellenverfahrens , 1962 .

[124]  Masuji Uemura,et al.  Buckling of Cylindrical Shell under Linearly-Varying Lateral Pressure , 1971 .

[125]  Franz G. Rammerstorfer,et al.  Storage Tanks Under Earthquake Loading , 1990 .

[126]  C. D. Babcock,et al.  Plastic buckling of cylindrical shells under biaxial loading , 1991 .

[127]  James G.A. Croll Towards a rationally based elastic-plastic shell buckling design methodology , 1995 .

[128]  Long-yuan Li,et al.  Elastoplastic dynamic instability of long circular cylindrical shells under pure bending , 1994 .

[129]  Richard Vynne Southwell,et al.  On the General Theory of Elastic Stability , 1914 .

[130]  Jurica Sorić,et al.  Stability analysis of a torispherical shell subjected to internal pressure , 1990 .

[131]  R. L. Roche,et al.  Experimental Tests on Buckling of Torispherical Heads and Methods of Plastic Bifurcation Analysis , 1986 .

[132]  G D Galletly,et al.  Buckling strength of imperfect steel hemispheres , 1995 .

[133]  Victor I. Weingarten The Buckling of Cylindrical Shells Under Longitudinally Varying Loads , 1962 .

[134]  Wei Zhang,et al.  Asymptotic solution for buckling of toroidal shells , 1991 .

[135]  R. A. Uras,et al.  Dynamic buckling of liquid-filled shells under horizontal excitation , 1990 .

[136]  Carlo Poggi,et al.  Stochastic imperfection modelling in shell buckling studies , 1995 .

[137]  Ekkehard Ramm,et al.  Buckling and imperfection sensitivity in the optimization of shell structures , 1995 .

[138]  Long-yuan Li Influence of loading imperfections on the stability of an axially compressed cylindrical shell , 1990 .

[139]  Eugene E Lundquiest Strength Tests of Thin-Walled Duralumin Cylinders in Combined Transverse Shear and Bending , 1935 .

[140]  David Bushnell,et al.  Elastic-plastic bending and buckling of pipes and elbows , 1981 .

[141]  B. O. Almroth,et al.  Influence of Edge Conditions on the Stability of Axially Compressed Cylindrical Shells , 1966 .

[142]  Eugene E Lundquist,et al.  Strength Tests on Thin-Walled Duralumin Cylinders in Torsion , 1932 .

[143]  D. N. Moreton,et al.  Internally Pressurized Machined Domed Ends—a Comparison of the Plastic Buckling Predictions of the Deformation and Flow Theories , 1990 .

[144]  C. D. Babcock,et al.  Buckling of Oil Storage Tanks in SPPL Tank Farm During the 1979 Imperial Valley Earthquake , 1984 .

[145]  J. M. Rotter,et al.  Non-symmetric bifurcation of geometrically nonlinear elastic-plastic axisymmetric shells under combined loads including torsion , 1989 .

[146]  Viggo Tvergaard Plastic buckling of axially compressed circular cylindrical shells , 1983 .

[147]  C. Chao,et al.  Buckling of a Thin-Walled Circular Cylindrical Shell Heated Along an Axial Strip , 1964 .

[148]  Nicholas J Hoff,et al.  THE PERPLEXING BEHAVIOR OF THIN CIRCULAR CYLINDRICAL SHELLS IN AXIAL COMPRESSION , 1966 .

[149]  A. E. Elwi,et al.  Ultimate shear strength of large diameter fabricated steel tubes , 1992 .

[150]  Marios K. Chryssanthopoulos,et al.  Imperfection Modeling for Buckling Analysis of Stiffened Cylinders , 1991 .

[151]  J. M. Bozajian,et al.  Creep Buckling of Cylindrical Shells in Axial Compression , 1957 .

[152]  C. Pearson General theory of elastic stability , 1956 .

[153]  Vasile G. Roman,et al.  Postbuckling Shear Capacity of Thin Steel Tubes , 1988 .

[154]  P. L. Gould,et al.  Local-global analysis on localized non-linear shells of revolution , 1994 .

[155]  C. G. Foster,et al.  Multiple geometric defects: Their effect on stability of cylindrical shells , 1991 .

[156]  Ekkehard Ramm,et al.  Buckling of Shells , 1982 .

[157]  C. Bert,et al.  Buckling of cylindrical and conical sandwich shells with orthotropicfacings. , 1968 .

[158]  A. E. Elwi,et al.  Tests of fabricated steel cylinders subjected to transverse loads , 1992 .

[159]  Rakesh K. Kapania,et al.  Dynamic buckling of imperfection-sensitive shell structures , 1987 .

[160]  Hui‐Shen Shen,et al.  Buckling and postbuckling behaviour of cylindrical shells under combined external pressure and axial compression , 1991 .

[161]  J. M. Rotter,et al.  Recent research on the behaviour and design of steel silo hoppers and transition junctions , 1992 .

[162]  Walter Wunderlich,et al.  Imperfection sensitivity of elastic and elastic-plastic torispherical pressure vessel heads , 1994 .

[163]  G. Fischer,et al.  Influence of boundary conditions on stability of thin-walled cylindrical shells under axial load and internal pressure , 1965 .

[164]  R. H. Gallagher,et al.  Elastic Instability of a Cylindrical Shell Under Arbitrary Circumferential Variation of Axial Stress , 1960 .

[165]  Stelios Kyriakides,et al.  Experimental Determination of the Propagation Pressure of Circular Pipes , 1981 .

[166]  L. Donnell,et al.  Effect of Imperfections on Buckling of Thin Cylinders and Columns under Axial Compression , 1950 .

[167]  T. Weller,et al.  Experimental Studies on the Buckling Under Axial Compression of Integrally Stringer-Stiffened Circular Cylindrical Shells , 1977 .

[168]  Sukhvarsh Jerath,et al.  Buckling of Orthotropic Cylinders Due to Wind Load , 1985 .

[169]  Shun Cheng,et al.  Buckling of Locally Loaded Isotropic, Orthotropic, and Composite Cylindrical Shells , 1988 .

[170]  J. Michael Rotter,et al.  Elastic Stability of Lap‐Jointed Cylinders , 1989 .

[171]  G D Galletly,et al.  Stability of Complete Circular and Non-Circular Toroidal Shells , 1995 .

[172]  B. Geier,et al.  Flat bar steel ring stiffeners on cylinders subjected to external pressure , 1993 .

[173]  Marios K. Chryssanthopoulos,et al.  Statistical Analysis of Imperfections in Stiffened Cylinders , 1991 .

[174]  T. S. Hull,et al.  Wall loads in squat steel silos during earthquakes , 1989 .

[175]  Thomas Ummenhofer,et al.  On the modelling of different types of imperfections in silo shells , 1995 .

[176]  Lars Å. Samuelson,et al.  Design of shell structures with openings subjected to buckling , 1991 .

[177]  N. W. Murray,et al.  Local buckling of thin-walled pipes being bent in the plastic range , 1992 .

[178]  Lynn S. Beedle Stability of Metal Structures: A World View , 1991 .

[179]  Manuel Stein The Effect on the Buckling of Perfect Cylinders of Prebuckling Deformations and Stresses Induced by Edge Support , 1962 .

[180]  W. T. Koiter THE STABILITY OF ELASTIC EQUILIBRIUM , 1970 .

[181]  W. T. Koiter,et al.  Buckling of an axially compressed cylindrical shell of variable thickness , 1994 .

[182]  Jørgen Juncher Jensen,et al.  Buckling behaviour of imperfect spherical shells subjected to different load conditions , 1995 .

[183]  J. Bkachut,et al.  Combined axial and pressure buckling of shells having optimal positive Gaussian curvature , 1987 .

[184]  Jan Błachut,et al.  Buckling Design of Imperfect Welded Hemispherical Shells Subjected to External Pressure , 1991 .

[185]  Xiaoli Ding,et al.  The Measurement of Imperfections in Cylindrical Silos for Buckling Strength Assessment , 1992 .

[186]  Lars Å. Samuelson Effect of Local Loads on the Stability of Shells Subjected to Uniform Pressure Distribution , 1992 .

[187]  Jan Bielski Influence of geometrical imperfections on buckling pressure and post-buckling behavior of elastic toroidal shells , 1992 .

[188]  Tanchum Weller,et al.  Combined stiffening and in-plane boundary conditions effects on the buckling of circular cylindrical stiffened-shells☆ , 1978 .

[189]  George J. Simitses,et al.  Imperfection sensitivity of fiber-reinforced, composite, thin cylinders , 1985 .

[190]  W. C. Schnobrich Thin Shell Structures , 1985 .

[191]  Susumu Toda,et al.  Buckling of cylinders with cutouts under axial compression , 1983 .

[192]  M. R. Horne,et al.  The Behaviour of Circular Tubes with Large Openings Subjected to Axial Compression , 1981 .

[193]  Ahmed K. Noor,et al.  Bibliography of Monographs and Surveys on Shells , 1990 .

[194]  Sunil Saigal,et al.  Advances of thin shell finite elements and some applications—version I , 1990 .

[195]  David Durban,et al.  Elastoplastic Buckling of Annular Plates in Pure Shear , 1989 .

[196]  R. Narayanan Shell Structures: Stability and Strength , 1990 .

[197]  Herbert E. Lindberg,et al.  Dynamic Pulse Buckling of Imperfection-Sensitive Shells , 1991 .

[198]  Stelios Kyriakides,et al.  Bifurcation Buckling Versus Limit Load Instabilities of Elastic-Plastic Tubes Under Bending and External Pressure , 1990 .

[199]  W. Guggenberger,et al.  Proposed Design Rule for Buckling Strength Assessment of Cylindrical Shells under Local Axial Loads , 1993 .

[200]  Jurica Sorić,et al.  Imperfection sensitivity of internally-pressurized torispherical shells , 1995 .

[201]  David Durban,et al.  Elastoplastic buckling of axially compressed circular cylindrical shells , 1992 .

[202]  Xiaoli Ding,et al.  The Measurement of Imperfections in Full-scale Steel Silos , 1992 .

[203]  S C Palmer Structural Effects of Foundation Tilt on Storage Tanks , 1992 .

[204]  J. Michael Rotter,et al.  Buckling of Pressurized Axisymmetrically Imperfect Cylinders under Axial Loads , 1992 .

[205]  Graham L. Hutchinson,et al.  Buckling considerations in the design of elevated steel water tanks , 1990 .

[206]  J. Tani,et al.  Dynamic stability of liquid‐filled cylindrical shells under vertical excitation, Part I: Experimental results , 1987 .

[207]  C. R. Calladine,et al.  Buckle propagation in submarine pipelines , 1988 .

[208]  Aviv Rosen,et al.  The Influence of Boundary Conditions on the Buckling of Stiffened Cylindrical Shells , 1976 .

[209]  R. Greiner,et al.  Buckling of Wind Loaded Cylindrical Shells — Application to Unstiffened and Ring-Stiffened Tanks , 1982 .

[210]  W. Flügge,et al.  Die Stabilität der Kreiszylinderschale , 1932 .

[211]  A. S. Tooth,et al.  A study of the stability of horizontal cylindrical vessels filled with varying amounts of liquid— Part I: Experimental investigations , 1983 .

[212]  D. Bushnell Plastic Buckling of Various Shells , 1982 .

[213]  Srinivasan Sridharan,et al.  A local–global model for the non‐linear analysis of locally defective shells of revolution , 1994 .