In this paper we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational inequality for the displacement field. We prove the unique weak solvability of the problem, then we state and prove some convergence results, for which we provide the corresponding mechanical interpretation. Next, we turn to the numerical approximation of the problem based on a finite element scheme. We use a relaxation method to solve the discrete problems that we implement on the computer. Using this method, we provide numerical simulations which validate our convergence results.

翻译：本文研究了一个描述两根弹性杆附着于非线性弹簧时平衡状态的数学模型。我们推导了该模型的变分形式，其表现为关于位移场的椭圆型拟变分不等式。证明了问题的唯一弱可解性，随后陈述并证明了一些收敛性结果，并给出了相应的力学解释。接着，我们基于有限元方法对该问题进行了数值逼近。采用松弛法求解离散问题并在计算机上实现。利用此方法，我们提供了数值模拟结果，验证了收敛性结论。