A Direct analysis of elastic contact using super elements

Abstract

Solutions to contact problems are important in mechanical as well as in civil engineering, and even for the most simple problems there is still a need for research results. In the present paper we suggest an alternative finite element procedure and by examples show the need for more knowledge related to the compliance of contact surfaces. The most simple solutions are named Hertz solutions from 1882, and we use some of these solutions for comparison with our finite element results. As a function of the total contact force we find the size of the contact area, the distribution of the contact pressure, and the contact compliance. In models of finite size the compliance depends on the flexibility of the total model, including the boundary condition of the model, and therefore disagreement with the locally based analytical models is expected and found. With computational contact mechanics we can solve more advanced contact problems and treat models that are closer to physical reality. The finite element method is widely used and solutions are obtained by incrementation and/or iteration for these non-linear problems with unknown boundary conditions. Still with these advanced tools the solution is difficult because of extreme sensitivity. Here we present a direct analysis of elastic contact without incrementation and iteration, and the procedure is based on a finite element super element technique. This means that the contacting bodies can be analyzed independently, and are only coupled through a direct analysis with low order super element stiffness matrices. The examples of the present paper are restricted to axisymmetric problems with isotropic, elastic materials and excluding friction. Direct extensions to cases of non-isotropy, including laminates, and to plane and general 3D models are possible.