Influence of physical and geometrical nonlinearity on the value of the upper critical pressure in buckling of a hollow sphere

Abstract

The framework of the Murnaghan model of a nonlinearly elastic body is used to investigate the problem of stability of a closed sphere acted upon by hydrostatic pressure. The theory of small deformations of an elastic body superimposed on a finite deformation is used [1]. The initial stress-strain state of equilibrium of the sphere is assumed to be centrally symmetric, and the neighboring state of equilibrium to be axisymmetric. The conditions of bifurcation of equilibrium lead to an eigenvalue problem with a nonlinear entry of the parameter. A solution of this problem is obtained by numerical methods for spheres of varying thickness, with various constants appearing in the equation of state taken into account. Several variants of the equations of neutral equilibrium are compared, depending on the accuracy of solution of the initial problem. All this makes possible the investigation of the influence of the physical and geometrical nonlinearity on the value of the critical pressure to be carried out.