On the finite element solution of the three-dimensional tire contact problem

Starting from a theoretical analysis of the static contact problem 'deformable body-rigid object' various solutions including the three-dimensional pneumatic tire contact problem are being discussed. The computed shapes and sizes of the footprint area as well as the load-deflection response are in good agreement with experimental results. The following approaches for a numerical solution are presented in this paper: (1) Elimination method: This method is based on using the influence coefficient technique to compute the nodal forces as well as the footprint area by iteration applying a geometrical linear or nonlinear FE technique. (2) 'Nonlinear Programming' technique: Recent developments in the theory of nonlinear optimization in abstract spaces suggest to describe the contact problem by a constrained optimization problem in function spaces. The minimization of the potential energy of the elastic body, the rigid obstacle being replaced by an operator constraint depending on the displacement functions, leads to three necessary conditions determining completely the equations of equilibrium, the contact zone and the pressure distributions in the contact zone. This result justifies the use of a nonlinear programming code to solve the discrete problem approximated by the method of finite elements. (3) Variation of boundary conditions: This method is based on an incremental formulation including nonlinear geometry and variable boundary conditions. (orig.)