并行有限元计算中的接触算法

A CONTACT ALGORITHM FOR PARALLEL COMPUTATION OF FEM

针对动态接触问题的有限元并行计算,提出了一种新的接触算法．新算法引入局部拉氏乘子技术来计算接触力．由于同时考虑了无穿透的接触约束条件和相邻接触对的相互影响,较之广泛使用的罚参数法,新算法使接触约束条件和系统平衡方程得到更充分的满足．虽然为提高接触计算精度而在局部采用了迭代技术,但算法仍然具有较高的效率,且与显式时间积分方案完全相容．此外,通过构造专门的区域分解方案,实现了将现有为串行程序开发的搜索算法平滑移植到并行环境的目标．数值算例表明,所提出的接触算法具有很好的并行性,在保证了接触问题并行计算精度的同时,取得了满意的并行效率．

A general contact algorithm for parallel finite element simulation of dynamic contact problem is presented in this paper. The local Lagrange multiplier approach is used in the new contact algorithm. Since the impenetrability condition and the interaction of adjacent contact pairs are all considered in this algorithm, the contact constraint and equilibrium equations of the system are better satisfied as compared with the traditional penalty method. Although some local iterations have to be done, the algorithm has a high computational efficiency, and is totally consistent with the explicit time integration. In addition, the existing contact search algorithms developed for serial finite element programs could be transfered into the parallel finite element program without any modification by the design of a special domain decomposition scheme. Numerical examples show that the new contact algorithm is effective for parallel finite element computations. The new algorithm ensures not only a good simulation accuracy, but also a high parallel-execution efficiency.