Abstract
The classical method of Hertz fails to approximate the relative approach of bodies in a state of plane strain or plane stress induced by their mutual contact. The method also fails to provide a uniform approximation to the displacement field over an entire body. In this paper, the method of Hertz is interpreted in terms of modern perturbation theory. The relative approach is found for frictionless contact between a pair of elastic, circular cylinders which have differing radii and properties. A composite asymptotic expansion of the displacement field is developed, which is uniformly valid over both the neighborhood of the contact surface and the remainder of a body. The method employed in this paper may be applied to a wide variety of contact problems.
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