Finite Elastic Deformations of a Tyre Modelled as an Ideal Fibre-Reinforced Shell

ISSN： 0374-3535

Source： Journal of Elasticity, Vol.54, Iss.1, 1999-01, pp. : 43-71

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Abstract

Vehicle tyres are anisotropic inhomogeneous fibre-reinforced shells which undergo finite elastic deformations. Calculation of their stress and deformation fields is a difficult task and is normally performed using the finite element technique. In this paper an attempt is made to provide an approximate analysis of the deformation field modelling the tyre as an ideal fibre-reinforced material. Radial-ply tyres are reinforced by a ’belt‘ of fibres running around the wheel in the circumferential direction under the tread of the tyre. A second set of fibres lies in each radial cross-section, of the tyre and runs from the bead wire which seats against one wheel rim to the bead wire at the other wheel rim. We shall assume each radial cross-section of the tyre is in a state of plane strain and is formed from an arch of fibre-reinforced composite material which is reinforced in the ’hoop‘ direction. This composite is assumed to be an ’ideal‘ material which is inextensible in the fibre-direction and is incompressible. The plane-strain deformations of this section are examined and then used to analyse the deformation of the tyre as a whole.