A numerical method to solve the normal and tangential contact problem of elastic bodies

Recently, interest has been growing among the engineering community to develop predictive models for the effect of joints on the tribology of jointed structures. The ability to predict contact forces and force–displacement relations of joints is key in enabling simulations to predict forced response and wear of jointed structures. Only for a limited number of contact geometries has a solution in closed-form been found, and it is available in the literature. The finite element method has been used to a great extent to solve problems of elastic bodies in contact, but the iterative solution of large models is very demanding. This work deals with the development of a numerical procedure that utilizes the stiffness matrices of the bodies in contact modeled with the finite element method. The matrices are reduced with a lossless static reduction, and their small dimensions make the iterative solution of the contact problem very fast. Results are compared with contact models found in the literature and the sample results agree well with corresponding analytical solutions.