We propose an enriched finite element formulation to address the computational modeling of contact problems and the coupling of non-conforming discretizations in the small deformation setting. The displacement field is augmented by enriched terms that are associated with generalized degrees of freedom collocated along non-conforming interfaces or contact surfaces. The enrichment strategy effectively produces an enriched node-to-node discretization that can be used with any constraint enforcement criterion; this is demonstrated with both multiple-point constraints and Lagrange multipliers, the latter in a generalized Newton implementation where both primal and Lagrange multiplier fields are updated simultaneously. The method's ability to ensure continuity of the displacement field -- without locking -- in mesh coupling problems, and to transfer fairly accurate tractions at contact interfaces -- without the need for contact stabilization -- is demonstrated by means of several examples. In addition, we show that the formulation is stable with respect to the condition number of the stiffness matrix by using a simple Jacobi-like diagonal preconditioner.
翻译:我们提出一个浓缩的有限要素配方,以解决接触问题的计算模型和小变形环境中不兼容的离散的组合。变换场由与不兼容的界面或接触表面相连接的自由普遍程度相关联的浓缩条件来增加。浓缩战略有效地产生了一种浓缩的节点到节点的离散,可用于任何强制执行标准;这通过多点限制和拉格朗格乘数来证明,后者在普遍牛顿实施中,原始和拉格朗倍增场都同时更新。确保变换场的连续性 -- -- 在网状组合问题中不锁定 -- -- 的方法,以及在接触界面转移相当准确的牵引 -- -- 不需要接触稳定 -- -- 的能力通过几个例子来证明。此外,我们通过使用简单的雅各比式的对角前置装置来显示,这种配方在坚硬度矩阵的状态上是稳定的。