Contact solutions for a circular orthotropic beam accounting for transverse normal strain

A higher order orthotropic circular beam theory, which accounts for radial and circumferential normal strain, as well as deformations due to transverse shearing and bending, is developed using the principle of virtual work. As such, the governing differential equations are expressed in terms of the four independent stiffness quantities, EA1, EA2, GA and EI. Special cases that can be obtained by appropriate limits include a Timoshenko beam (GA, EI) and an Euler beam (EI) with or without axial extension (EA2). Using these equations the frictionless contact problem of a compressed ring is solved analytically and the significance of transverse normal strain is studied by comparing with solutions from the more elementary beam theories. Furthermore, the limitations of these theories are studied through comparison with plane elasticity solutions obtained using finite elements. The effect of the radial stiffness (EA1) on the contact pressure is quantified and shown to be important for many practical problems, such as a tire that includes the effect of a tread.