Collected Works of H. S. Tsien (1938-1956)

The Buckling of Spherical Shells by External Pressure*

Th. von Kármán and Hsue-shen Tsien

(California Institute of Technology)

The general theory of thin shells was developed by A. E. H. Love. He assumed small deflections and for that reason neglected in the energy expression all terms higher than quadratic, and thus obtained linear differential equations for the determination of the equilibrium position of a shell under given forces. The theory of buckling of thin shells is also based essentially on Love’s equations. The buckling of cylindrical shells of uniform thickness under the action of a uniformly distributed axial load was calculated by R. Lorentz, R. V. Southwell, S. Timoshenko, W. Flügge, L. H. Donnell, and others. The same problem ...