Free and constrained inflation of elastic membranes in relation to thermoforming — axisymmetric problems

Abstract

Thermoforming of a heated polymeric membrane by pressure inflation against a relatively cold mould surface presents a class of large deformation stress analysis problems in which account must be taken of the progressively changing boundary conditions caused by the sheet coming into contact with the mould surface. As a first step towards solving the general problem, the paper presents a finite element formulation for stress analysis under axisymmetric conditions. Analysis results are presented for free and constrained inflation of a flat circular membrane, the latter with respect to inflation against (a) a circular cylindrical surface, (b) a 60 degree conical surface, and (c) a horizontal plate. As reasonable physical approximations, the material is considered to be purely elastic while the contact conditions are idealized to be either friction-less or non-slipping. Analysis results are compared with those obtained by experiments on rubber membranes.