A complementary principle of elastic bodies of arbitrary geometry in rolling contact

In the study a complimentary principle of three-dimensional elastic bodies in rolling contact is derived in detail. The boundary conditions outside the contact area of the bodies, the curved contact area and the real geometry sizes of the bodies are taken into consideration in the complimentary principle. In fact it is a generation of Kalkerʹs theoretical model of three-dimensional elastic bodies in rolling contact. The new theoretical model in this paper is more available for the analysis of general rolling contact, and it avoids the assumptions of elastic half space and approximate contact area of plane adopted in the existing theories of rolling contact. Finally the main points of numerical implementation of the problem are also given in the paper.