A new method to analyze two-body contact problems in linear elasticity using a virtual displacement technique and solution to the elastic boundary value problems for a curved half-space

The accepted procedure for the analysis of two linearly elastic bodies in contact is to utilize the techniques developed by H. Hertz in 1882.;In the development of these techniques, several simplifying assumptions were made. These assumptions restrict the geometry of each of the bodies to be analyzed to simple curves with two perpendicular principle radii. In addition, the resultant stress profile is expressly assumed to be elliptical in nature.;The methods developed in this dissertation utilize a virtual displacement technique to transform the two body contact problem into a single body elastic boundary value problem with assumed surface displacements. This in turn is solved by developing an extension of the Boussinesq and Cerruti solutions for planar elastic half-spaces. This procedure consists of transforming the required equations into an orthogonal curvilinear coordinate system.;To validate the new method, two problems are analyzed which fit well within the limitations of the current Hertz theory. The results of the calculations using the new method are compared directly to the existing Hertz method, and show excellent agreement. The two problems analyzed are contact between a cylinder and a sphere, and contact between two spheres.;In order to demonstrate that the new method is capable of solving problems that the Hertz theory is not capable of solving, the contact between a sphere and a parabolic shape is analyzed.