Technical Brief: Knockdown Factor for the Buckling of Spherical Shells Containing Large-Amplitude Geometric Defects

We explore the effect of precisely defined geometric imperfections on the buckling load of spherical shells under external pressure loading, using finite element analysis that was previously validated through precision experiments. Our numerical simulations focus on the limit of large amplitude defects and reveal a lower bound that depends solely on the shell radius to thickness ratio and the angular width of the defect. It is shown that, in the large amplitude limit, the buckling load depends on an single geometric parameter, even for shells of moderate radius to thickness ratio. Moreover, numerical results on the knockdown factor are fitted to an empirical, albeit general, functional form that may be used as robust design guideline for the critical buckling conditions of pressurized spherical shells.

[1]  Shigeo Kobayashi.  The influence of the boundary conditions on the buckling load of cylindrical shells under axial compression , 1968 .

[2]  A. E. Johnson,et al.  Experimental investigation of the buckling instability of monocoque shells , 1961 .

[3]  H. Tsien.  A Theory for the Buckling of Thin Shells , 1942 .

[4]  Mark W. Hilburger,et al.  Developing the Next Generation Shell Buckling Design Factors and Technologies , 2012 .

[5]  L. Seaman.  THE NATURE OF BUCKLING IN THIN SPHERICAL SHELLS , 1962 .

[6]  T. Kármán,et al.  The Buckling of Spherical Shells by External Pressure , 1939 .

[7]  P. Reis,et al.  Fabrication of slender elastic shells by the coating of curved surfaces , 2016, Nature Communications.

[8]  J. Hutchinson,et al.  The Geometric Role of Precisely Engineered Imperfections on the Critical Buckling Load of Spherical Elastic Shells , 2016 .

[9]  Tatsuzo Koga,et al.  The axisymmetric buckling of initially imperfect complete spherical shells , 1969 .

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

[11]  P. Seide,et al.  Buckling of thin-walled circular cylinders , 1968 .

[12]  J. Hutchinson.  Buckling of spherical shells revisited , 2016, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[13]  Mark W. Hilburger,et al.  Shell Buckling Design Criteria Based on Manufacturing Imperfection Signatures , 2003 .

[14]  W. T. Koiter.  Over de stabiliteit van het elastisch evenwicht , 1945 .

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

[16]  Isaac Elishakoff.  Resolution of the Twentieth Century Conundrum in Elastic Stability , 2014 .

[17]  John W. Hutchinson,et al.  Buckling of circular cylindrical shells under axial compression. , 1972 .

[18]  L. Mahadevan,et al.  Localized and extended deformations of elastic shells , 2008, Proceedings of the National Academy of Sciences.

[19]  T. Kiernan,et al.  Elastic stability of near-perfect shallow spherical shells , 1963 .

[20]  Rolf Zimmermann,et al.  Geometric imperfections and lower-bound methods used to calculate knock-down factors for axially compressed composite cylindrical shells , 2014 .

[21]  Lars A. Samuelson,et al.  Shell Stability Handbook , 2014 .

[22]  Robert Zoelly,et al.  Ueber ein Knickungsproblem an der Kugelschale , 1915 .

[23]  E. Riks.  An incremental approach to the solution of snapping and buckling problems , 1979 .

[24]  Y. Fung,et al.  A nonlinear theory of bending and buckling of thin elastic shallow spherical shells , 1954 .