Problems of elastic frictional contact are of great engineering relevance playing major roles in many fields such as tribology, attachment integrity, and even structural dynamics. These problems are historically extremely difficult to analyze either theoretically or numerically. A quick review of the literature provides insight as to a major cause of the numerical difficulty specifically that traditional algorithms search for contact solutions that satisfy all equality and inequality constraints using iterative processes that pass through states that do not satisfy those constraints and are physically inadmissible. A novel contact algorithm - the Method of First Violation - is introduced to address the deficiency identified in traditional methods by choosing load steps precisely so as to avoid iterations through inadmissible states. The new algorithm is demonstrated on multiple contact problems and the results compared to those of a conventional algorithm and to analytic solutions where available. Finally, the Method of First Violation is demonstrated on a contact problem with a nontraditional friction model (Dahls model) to demonstrate generality and robustness.

弹性摩擦接触问题在许多领域都具有重要的工程意义，例如摩擦学，附着完整性，甚至结构动力学。这些问题在历史上无论从理论上还是从数值上都很难分析。对文献的快速回顾提供了有关数值困难的主要原因的见解，特别是传统算法使用经过不满足那些约束且物理上不可接受的状态的迭代过程来搜索满足所有等式和不等式约束的接触解。引入了一种新颖的接触算法-首次违规方法-通过精确选择载荷步长来避免传统方法中发现的缺陷，从而避免由于不允许的状态而引起的迭代。该新算法针对多种接触问题进行了演示，并将结果与​​常规算法的结果以及可用的解析解决方案进行了比较。最后，在非传统摩擦模型（达尔斯模型）的接触问题上论证了初次违法方法，以证明其通用性和鲁棒性。