板带轧制过程二维流函数-无网格伽辽金求解方法及其应用

发布时间：2018-05-01 14:43

本文选题：无网格伽辽金法 + 流函数　；参考：《机械工程学报》2015年10期

【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。
[Abstract]:In view of the problems of low computational efficiency and relatively complicated boundary treatment in solving the plastic deformation of plate and strip rolling process by element free Galerkin method EFGM without meshless Galerkin method, the basic solution idea and frame of EFGM are retained. A two-dimensional meshless method, flow function-element free Galerkin method (Flow function-element free Galerkin method) for plate and strip rolling process, is derived by introducing the flow function into EFGM. In this method, the value of the nodal flow function in the domain is taken as the unknown variable, the velocity field is derived by the flow function, and then the other field quantities are solved, and the order reduction of the stiffness matrix is realized. Using the stream function as the unknown basic variable can not only satisfy the volume incompressibility condition automatically, but also make it easier to apply the essential boundary condition and friction boundary condition. In order to verify the method, the two-dimensional plane-strain rolling process is modeled and simulated. It is found that the computational efficiency is much higher than that of the original EFGM, and the calculated results are in good agreement with the rigid-plastic finite element results of classical literatures and the measured results in the literature.
【作者单位】：北京科技大学机械工程学院;
【基金】：国家自然科学基金资助项目(51075031,51174248)
【分类号】：TG335.5

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