Stability of relatively deep segments of spherical shells loaded by external pressure

Abstract

The buckling of shells in the form of spherical segment depends strictly on its rise. Determination of full equilibrium paths for shells of higher rise is very laborious and evokes many numerical problems. Spherical caps loaded by the external pressure and clamped along the base circle are the subject of a detailed analysis. The stability analysis for shells of relative slenderness of interval λ=3.5–12 was performed and is presented in the paper. Three critical points, and namely the primary bifurcation point, the primary higher limit point and the primary lower limit point were basis for the plot of relative critical pressure versus slenderness parameter. This plot has big practical significance. One can read off from it the value of critical pressure being the basis of designing procedure, which takes into account stability criterion. The author's program based on FEM and taking into account all singularities characteristic for nonlinear elastic stability, was used in calculations. The correctness of the approach was verified on the example of spherical segment of slenderness λ=8 solved before by other authors.