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The pneumatic tire has proven to be the dominant design for rolling transport since shortly after its invention by John Boyd Dunlop in 1888. This paper identifies four critical characteristics that led to the success of the pneumatic tire: low energy loss on rough surfaces, low vertical stiffness, low contact pressure, and low mass. A non-pneumatic structure is proposed that exhibits these four critical characteristics while breaking some of the most restrictive design constraints imposed by pneumatic mechanics. This structure consists of a circular beam composed of two inextensible membranes separated by a relatively low modulus elastic material. The beam is connected to a hub by thin elastic spokes. This structure forming an integrated tire∕wheel is called a Tweel™.

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a b s t r a c tContact of a circular ring with a flat, rigid ground is considered using curved beam theory and analytical methods. Applications include tires, springs, and stiffeners, among others. The governing differential equations are derived using the principle of virtual work and the formulation includes deformations due to bending, transverse shear and circumferential extension. The three associated stiffness quantities, EI, GA and EA, respectively, remain as independent parameters in the differential equations. This allows the special cases such as an inextensible Timoshenko beam (EI and GA) or an extensible Euler beam (EI and EA) to be obtained directly by the appropriate limits. The effect of these three stiffness parameters on the contact pressure solution is studied, which shows how those fundamental parameters can be selected for the purpose of the application. Although the formulation is for small displacement theory, both radial and circumferential distributed loads are considered, which allows the pressure in the deformed state to be vertical rather than radial, which is shown to be important. Closed form expressions for all force and displacement quantities are obtained in terms of the angular location of the edge of contact, which must be determined numerically. Extensibility complicates the analytical expressions within the contact region, and a series solution is proposed in this case. A two-term asymptotic expression for the stiffness of the ring is determined analytically. Finally, all solutions are validated using the commercial finite element software ABAQUS, with attention to non-linear behavior and the range of validity of these solutions.

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