The coefficient of buckling pressure of spherical-cap and spherical shell has been found out on the oblate shell theory. This roefficient demonstrates that the buckling pressure take either the upper limit value or the lower limit value according to the state of deformation of spherical-cap and spherical shell just before the moment of buckling. The results of the experiments usually accord with the lower limit.
There is great difference between the testing results and classical stability theory value of spherical shell subjected to hydrostatic pressure. It is a difficult problem to find a theoretical formula in stability theory in good agreement with test data. The solution of this problem is of significant both in theory and application. We believe that the buckling area of spherical shell may be treated as a spherical-cap with a circle boundary. Under the uniform pressure, bending deformation symmetrial about the apex of the spherical-cap take place. From this characteristic displacement function (w) can be obtained from eqs (I) and (2). When buckling occurs, the uniform pressure P becomes the buckling pressure (Pcr), we may get the coefficient of buckling pressure from the displacement function (Ii), this coefficient shows that the buckling pressure of a spherical-rap and a spherical shell has upper limit and lower limit values. The upper limit value is the same value calculated by classical stability theory.
The curve coordinate system of spherical-cap with circle boundary is assumed with the Line x of the meridian direction and line y of the latitude direction as shown in Fig. 1. From the symmetry of displacement the components (u) and (w) of displacement of a given point with coordinate (x) are of the function of the coordinate (x). and the latitude component of displacement (v) is zero.