In a wide range of practical problems, such as forming operations and impact tests, assuming that one of the contacting bodies is rigid is an excellent approximation to the physical phenomenon. In this work, the well-established dual mortar method is adopted to enforce interface constraints in the finite deformation frictionless contact of rigid and deformable bodies. The efficiency of the nonlinear contact algorithm proposed here is based on two main contributions. Firstly, a variational formulation of the method using the so-called Petrov-Galerkin scheme is investigated, as it unlocks a significant simplification by removing the need to explicitly evaluate the dual basis functions. The corresponding first-order dual mortar interpolation is presented in detail. Particular focus is, then, placed on the extension for second-order interpolation by employing a piecewise linear interpolation scheme, which critically retains the geometrical information of the finite element mesh. Secondly, a new definition for the nodal orthonormal moving frame attached to each contact node is suggested. It reduces the geometrical coupling between the nodes and consequently decreases the stiffness matrix bandwidth. The proposed contributions decrease the computational complexity of dual mortar methods for rigid/deformable interaction, especially in the three-dimensional setting, while preserving accuracy and robustness.
翻译:在一系列广泛的实际问题中,例如成形操作和撞击测试,假设接触机构中的一个是僵硬的,是物理现象的极好近似于物理现象。在这项工作中,采用了成熟的双重迫击炮法,以便在硬体和变形体的有限畸形无摩擦接触中加强界面限制。此处提议的非线性接触算法的效率基于两个主要贡献。首先,对使用所谓的Petrov-Galerkin计划的方法的变式配方进行了调查,因为它通过消除明确评价双重基函数的需要而大大简化了该方法。相应的第一级双级双级迫击炮内推法是详细介绍的。然后,特别侧重于通过使用支直线性线间推法来延长二级内推法的延伸,该套法严格保留了定质元素网格网格的几何度信息。第二,建议对每个联系节点所附的节点的节点或正态移动框架作出新的定义。它减少了结点之间的几何调,从而降低了硬性矩阵带宽。拟议的贡献降低了双级迫击炮的计算复杂性,同时,特别为固度/形形模制的精确度。