自适应无网格方法在弹塑性接触中的应用

Applying Adaptive Meshless Model to Solving Elasto-Plastic Contact Problems

应用h型自适应无网格方法对二维弹塑性接触问题进行研究。无网格方法结点排布灵活,计算中可根据需要增减结点,便于自适应分析,通过对弹塑性本构关系和弹塑性接触问题的阐述,给出了自适应无网格方法求解弹塑性接触问题的计算模型和程序流程。采用自适应方法分别对圆柱体弹塑性接触和粗糙表面弹塑性接触算例进行求解,并分别与其均匀密化解进行比较。结果表明,在同等条件下采用自适应无网格方法对弹性-理想塑性和弹塑性接触问题进行计算能在较小的计算耗费下取得较好的计算结果。

Aim. This paper forms a small but essential part of a project supported by NNSFC （National Natural Science Foundation of China）. Starting from Ref. 3 by Xiao et al, Refs. 4 and 5 by Liu et al, and Ref. 6 by Rossi et al, it supplies a computationally efficient method needed by the NNSFC project. In the full paper, we explain in some detail the application of the adaptive meshless model to solving elastoplastic contact problems; in this abstract, we just add some pertinent remarks to listing the three topics of explanation. The first topic is： solution to the elasto-plastic contact problem. In this topic, we point out that, in computing the adaptive meshless model, some nodes need to be removed or inserted for the convenience of adaptive analysis. The second topic is： applying the adaptive meshless model to solving the elasto-plastie contact problem. In this topic, we give the method＇s flow chart and its computing module＇s schematic, as shown in Fig. 1 in the full paper. The third topic is： numerical examples. In this topic, we apply the adaptive meshless model to solving two numerical examples. （1） the problem of contact between cylinder and plane and （2） the problem of contact between rough surface and plane. Calculated results, shown in Fig. 3 and Table 1 for the first example and Fig. 6 and Table 2 for the second example, show preliminarily that our adaptively refined solutions are about the same in precision as the uniformly refined solutions but are more efficient in that CPU time required is less by about 75-80%.