中文摘要：

该文基于了Kalker三维弹性体非Hertz滚动接触理论模型，考虑滚动接触物体具有曲面接触斑，利用有限元法，推导出物体柔度系数，即力与位移之间的关系，将理论模型转化为数学上的非线性规划问题。结合拉格朗日乘子法，求解非线性方程组，从而得到接触斑力学行为。该模型是考虑曲面接触斑三维弹性体滚动接触理论模型，考虑了滚动接触物体的真实几何尺寸和接触区外边界因素对滚动接触行为的影响。为解决任何几何形状弹性体滚动接触问题提供了方法。该文主要对二维问题的数值模拟，所得数据结果较为合理。并结合商业有限元软件计算结果对静态问题进行对比验证，两种模型的分析结果吻合的较好。该文的模型和数值方法进一步完善后将适用于任意曲面接触斑滚动接触问题的求解。

英文摘要：

Based on Kalker＇s Non-Hertz theoretical model of three-dimensional elastic bodies in rolling contact, this paper develops a new model for solving three-dimensional elastic bodies on rolling contact with the contact patch of curved surface, in which the influence exerted by the boundary conditions and arbitrary geometry of the bodies in roiling contact is taken into account. Finite element method （FEM） was used to discrete the elastic bodies in contact and calculate the flexibility coefficients between outside forces and displacements of the bodies. The theoretical model was transformed into a nonlinear programming problem which was solved by Lagrange multipliers method. The detailed numerical simulations of two-dimensional elastic bodies in static contact and with rotation around a fixed axis were carried out by using the present model. The results obtained were very reasonable. For the two-dimensional elastic bodies in static contact, the results obtained by the present model were compared with those by commercial finite element software. There was a good agreement between the results by the two methods. After the further improvement on the present theoretical model and numerical method, they can be used to analyze the complicated phenomena of rolling contact.