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通过移动最小二乘(MLS)近似函数建立无网格伽辽金法的基本公式。其中,本构关系基于Mises屈服准则和刚塑性流动理论给出,基函数采用线性函数。将无网格伽辽金法(EFG)与刚塑性流动理论相结合,编制了三维无网格伽辽金法数值模拟程序。进行铝合金三维体积成形试验,并用编制的模拟程序和ABAQUS有限元软件进行数值模拟。结果表明,无网格法与有限元法的数值模拟结果中的节点分布和等效塑性应变分布比较接近。通过对比数值模拟与试验结果验证了无网格伽辽金法数值模拟程序的可行性。
The basic formula of element - free Galerkin method is established by moving least square (MLS) approximation function. Among them, the constitutive relationship is given based on the Mises yield criterion and the rigid-plastic flow theory, and the basis functions are linear functions. The meshless Galerkin method (EFG) is combined with the rigid plastic flow theory to develop a three-dimensional meshless Galerkin numerical simulation program. Aluminum alloy three-dimensional volume forming test, and the use of simulation programs and ABAQUS finite element software for numerical simulation. The results show that the distribution of nodes and the equivalent plastic strain distribution in the numerical simulation results of meshless and finite element methods are close to each other. By comparing the numerical simulation and experimental results, the feasibility of the Galerkin numerical simulation program is verified.