Finite Element Analysis of the Tire Contact Problem

타이어 접지문제의 유한요소 응력해석

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 produced 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.

본 논문에서는 타이어의 각 부분의 물성치 계산을 위한 식을 유한요소법에 적용할 수 있도록 제안하였다. 이 식은 강철 코드의 굽힙효과를 고려 하였으며, 특히 각 요소에서 전단변형이 일어나는 동안의 굽힘효과를 고려하였다. 유한요소 공식화는 가상일의 원리에 의하여 평형 방정식으로부터 유도하였고, Updated refer- ence coordinate에 대해 증분해석을 적용하여 Updated Lagrangian공식화를 하였다. 그리고 차량하중에 의하여 타이어가 노면에 접지될때의 응력상태를 게산할 수 있도록 접촉문제 공식화를 유한요소 공식화에 첨가 하였다.