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A self-adaptive projection method for contact problems with the BEM

机译：BEM接触问题的自适应投影方法

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Highlights•A new and simple computational method is developed for the contact problem.•We use the variational method to analyze the convergence of proposed method.•We give the self-adaptive rule and the boundary element approximation for the method.•The performance of the method is demonstrated by the numerical results.AbstractA self-adaptive algorithm, based on the projection and boundary integral methods, is designed and analyzed for frictionless contact problems in linear elasticity. Using the equivalence between the contact problem and a variational formulation with a projection fixed point problem of infinite dimensions, we develop an iterative algorithm that formulates the contact boundary condition into a sequence of Robin boundary conditions. In order to improve the performance of the method, we propose a self-adaptive rule which updates the penalty parameter automatically. As the iteration process is given by the displacement and the stress on the boundary of the domain, the unknowns of the problem are computed explicitly by using the boundary element method. Both theoretical results and numerical experiments show that the method presented is efficient and robust.
机译： 突出显示 • 针对接触问题开发了一种新的简单计算方法。 • 我们使用变分方法来分析所提出方法的收敛性。 • 我们给自适应规则和该方法的边界元素近似。 • 数值结果证明了该方法的有效性。 摘要 基于投影和边界积分方法，针对线性弹性中的无摩擦接触问题，设计并分析了一种自适应算法。利用接触问题和具有无限维投影不动点问题的变分公式之间的等价关系，我们开发了一种迭代算法，将接触边界条件公式化为Robin边界条件序列。为了提高该方法的性能，我们提出了一种自适应规则，可以自动更新惩罚参数。由于迭代过程是由域边界上的位移和应力给出的，因此使用边界元方法显式计算了问题的未知数。理论结果和数值实验均表明该方法是有效且鲁棒的。

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