中文摘要：

针对无网格伽辽金法（Element free Galerkin method,EFGM）在求解板带轧制过程塑性变形时计算效率低及边界处理相对复杂等问题,在保留EFGM的基本求解思想与框架基础上,将流函数引入EFGM,推导建立一种针对板带轧制过程的二维无网格方法——流函数-无网格法（Flow function-element free Galerkin method,F-EFGM）。由于在该方法中,以求解域内各节点流函数值为未知变量,速度场通过流函数求导得到,进而求解其他场量,实现了对刚度矩阵的降阶。采用流函数作为未知基础变量不仅能自动满足体积不可压缩条件,还使本质边界条件和摩擦边界条件的施加更加简便。为考核验证该方法,建模并仿真分析二维平面应变轧制过程,发现计算效率比原EFGM大大提高,计算结果与经典文献的刚塑性有限元计算结果和文献中实测结果吻合较好。

英文摘要：

A new meshless method for calculating the plastic deformation of strip rolling process, which is named the flow function-element free Galerkin method abbreviated as F-EFGM, is developed based on the element free Galerkin method to overcome its low calculating efficiency and complexity in boundary treatment by inducing the flow function into the method. The velocities are partial derivatives of the flow function. The order of the stiffness matrix is decreased when the flow function instead of velocity at every node in the solution region becomes the main variable to be resolved. Besides, the boundary processing is more convenient since the volume invariability is automatically satisfied by inducing the flow function. In order to demonstrate the advantage of the new numerical method, the two dimensional strain rolling process is simulated and properly analyzed. The results show that the calculation efficiency is dramatically lifted compared to the original method. The validity of the new method is also verified by comparing the results to those with the rigid-plastic finite element method and some experimental observations in the references.