The tire inflation and contact problem has been solved by a finite element method. The finite element formulation is derived from the equilibrium equations by the principle of virtual work in the form of an updated Lagrangian formulation for incremental analysis. Then, a contact formulation is added to the finite element formulation to calculate stress state of tire in contact with flat rigid road under the load due to the self-weight of a vehicle. In the finite element analysis, equations of effective material properties are introduced to analyze a plane strain model of the shell-like tire by considering the bending effect of reinforced steel cords.
The proposed equations of effective material properties produces stress concentration around the edge of belt layers, which does not appear when other well-known equations of material properties are adopted.
The result from the above algorithm demonstrates the validity of the formulation and the proposed equations for the effective elastic constants. The result fully interprets the cause of separation between belt layers by showing the stress concentration.