On the axisymmetric buckling behaviour of incompressible nonlinearly elastic spherical shells

In this paper we study the axisymmetric quasistatic buckling behaviour of complete incompressible nonlinearly elastic spherical shells under hydrostatic pressure. The shells suffer flexure, shear, and mid-surface compression. Thickness changes occurring on the trivial solution are taken into account. The theory is geometrically exact; the description is based on a 3-dimensional model with an involved thickness parameter delta. The approach yields the pressure intensities at which bifurcation branches emanate, provides information about the qualitative and quantitative local solution behaviour and permits in some neighbourhood of the trivial solution a determination of the deformed shell configuration associated to the bifurcation modes. Numerical results are presented. (C) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.