中文摘要：

针对弹塑性接触问题所构造的等价变分不等式，解除了弹塑性本构状态约束方程和接触状态约束方程的约束．首先证明了所构造泛函的强制性，从而证明了所构造的等价变分不等式解的惟一性，并根据椭圆型变分不等式解存在的充分条件论证了弹塑性接触问题解的存在性，为该问题的变分极值原理的建立奠定了数学理论基础．所构造的变分极值形式为运用数学规划法求解弹塑性接触问题提供了理论保证．

英文摘要：

Contact problems and elastoplastic problems are unified and described by the variational inequality formulation, in which the constraints of the constitutional relations for elastoplastic materials and the contact conditions are relaxed totally. First, the coerciveness of the functional is proved. Then the uniqueness of the solution of variational inequality for the elastoplastic contact problems is demonstrated. The existence of the solution is also demonstrated according to the sufficient conditions for the solution of the elliptic variational inequality. A mathematical foundation is developed for the variational extremum principle of elastoplastic contact problems. The developed variational extremum forms can give an effective and strict mathematical modeling to solve contact problems with mathematical programming.