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将一种新的数值计算方法──无网格伽辽金法(Element-free Galerkin method,简称EFGM)用于三维斜轧穿孔过程的数值模拟。无网格伽辽金法采用移动最小二乘近似形函数,不满足Kronecker Delta函数性质,通过对形函数进行修正,使其能够直接转换为插值函数,从而可以直接施加本质边界条件。然后,给出了无网格伽辽金法斜轧穿孔计算模型及其详细的推导过程,采用双重收敛判据,得到了无网格伽辽金法计算结果。讨论了轧件的变形情况,并将场变量的计算结果与有限元计算结果进行了比较,分析了两者产生差别的原因。根据对比分析可知──运用无网格伽辽金法研究斜轧穿孔工艺是正确可行的。
A new numerical method, Element-free Galerkin method (EFGM), is used to simulate the three-dimensional cross-rolling process. Element-free Galerkin method uses the moving least square approximation function, which does not satisfy the Kronecker Delta function. By modifying the shape function, it can be directly converted into an interpolation function so that the essential boundary conditions can be directly applied. Then, the meshless Galerkin method and its derivation process are given. The meshless Galerkin method is used to obtain the results. The deformation of the rolling stock is discussed. The calculated results of the field variables are compared with those of the finite element method. The reasons for the difference between the two are analyzed. According to the comparative analysis, it can be seen that it is correct and feasible to use the element-free Galerkin method to study the cross-piercing process.