Effects of axisymmetric loads on inflated non-linear membranes

Abstract

This paper describes the effects of various external axisymmetric loads on pressurized hinged spherical membranes taking into account changes in internal pressure, volume, and temperature. “Exact” geometrical non-linearity along with generalized constitutive relations for a highly non-linearly clastic, isotropic, homogeneous, incompressible material are used in the analysis. The specialized case of a Hookean material is also treated. The non-linear equations of membrane equilibrium are derived in terms of additional finite displacements for the case of nonorthogonal curvilinear midsurface coordinates and are then specialized for the problem of an inflated hinged spherical membrane. The resulting two highly non-linear coupled second order differential equations are solved by means of a finite difference and Newton-Raphson iterative procedure. All results are presented in nondimensionalized graphical form.