Contact of an Inflated Toroidal Membrane with a Flat Surface as an Approach to the Tire Deflection Problem

Abstract

Abstract A finite element procedure has been developed for the displacement and stress analysis of a homogeneous and isotropic inner tube mounted on a rim and in contact with a flat surface. The geometric nonlinear effect is accounted for by including the quadratic terms in the strain-displacement equations. The nonlinear load-displacement path is predicted by a linear incremental procedure. The procedure is first demonstrated by a large deflection analysis of a strip of a tire (a cable). The results are in good agreement with a known alternative solution. A homogeneous and isotropic inner tube is then pressurized and the displacements and stresses are found. The displacements are also found experimentally. Both results are in good agreement. Finally, the inner tube is mounted on a rim and pressed against a rigid flat surface. The resulting displacements and footprints are also measured experimentally. The computer results are shown to be in reasonable agreement with the experiment.