Hertz’s contact theory is widely used in elastic solid contact problems. In this paper, the applicability of Hertz’s contact theory in conformal contact problems was examined. Taking deep groove ball bearing and the outer raceway model as an example, both the FEM analyses and the theoretical studies were conducted. It is found that when the radius coefficient of groove curvature is greater than 0.55, Hertz’s theory can be practically applied for conformal contact. Contact problems of rolling bearings are generally solved by Hertz’s contact theory without considering inclusions and inhomogeneities in the material. In this paper, inclusions are presented in the contact analyses, and the corresponding elastic field distribution of the contact-inclusion model is investigated by using the finite element method.

Failure localization in a variety of mechanical structures may be ascribed to elevated temperature, which may be effectively analyzed by employing the inclusion model. This work presents an explicit solution to the plane thermal inclusion problem, based on the customized Green’s function. A contour integral representation is further developed so as to provide an effective and straightforward approach for treating an arbitrarily shaped inclusion. Several benchmark examples are examined to validate the present solution.

The solution of the elastic field for inclusions in an elastic half space has been applied widely in many contact analyses and engineering designs. A popular method to solve the half-space inclusion problem resorts to the method of images, where the solution is decomposed into 3 components consisting of the full space inclusion, mirrored inclusion, and the surface traction cancellation. In the process of cancelling the redundant surface tractions determined from a full space inclusion problem, the computation domain is supposed to be limited in a finite size and there is inevitably truncation error. It has not been quantitatively investigated how the truncation error will influence the accuracy of the numerical computations based on the method of images. This work studies the deflection of the boundary surface of a half-space containing an Eshelby inclusion. Errors due to mesh refinement and domain truncation are quantitatively analyzed. Parametric studies are performed for a systematic examination of surface redundant tractions and their influences.

No abstract