本文根据变分不等方程理论论证了含摩擦弹性接触问题解的存在性和唯一性 ,并使其等价于二次规划问题。接触体系各部分离散后凝聚到接触边界上形成出口刚度矩阵 ,并根据接触面上法向位移的非穿透条件和摩擦律等条件 ,导出非负变量 υ,λ的线性互补方程。直接采用二次规划的 Lemke算法 ,其求解规模仅限于接触边界。榫齿模型接触分析结果和实验结果吻合较好。 According to the theory of variational inequality equations, this paper proves the existence and uniqueness of the solution to the problem of frictional elastic contact and makes it equivalent to the quadratic programming problem. After discrete parts of the contact system condense to the contact boundary to form exit stiffness matrix, linear complementary equations of non-negative variables υ and λ are deduced according to the non-penetration and friction laws of the normal displacement on the contact surface. The quadratic programming Lemke algorithm is used directly and its solution scale is limited to the contact boundary. Ten tooth model contact analysis and experimental results agree well.