中文摘要：

提出一种板材变形和软模体积变形耦合的数值分析方法。基于更新的拉格朗日（UL）列式，板材的弹塑性变形采用有限元法（FEM）分析，软模的体积变形采用无网格伽辽金法（EFGM）分析，板材和软模之间的摩擦接触通过罚函数法来处理。利用开发的有限元-无网格法耦合算法程序（CDSB-FEM-EFGM）分析板材弹性软模胀形过程。同有限元软件DEFORM-2D得到的数值解以及实验结果相比，验证了所开发程序的有效性。这种方法为分析板材软模成形提供了一种适合的数值方法。

英文摘要：

A numerical method for coupled deformation between sheet metal and flexible-die was proposed. Based on the updated Lagrangian （UL） formulation, the elastoplastic deformation of sheet metal was analyzed with finite element method （FEM） and the bulk deformation of flexible-die was analyzed with element-free Galerkin method （EFGM）. The frictional contact between sheet metal and flexible-die was treated by the penalty function method. The sheet elastic flexible-die bulging process was analyzed with the FEM-EFGM program for coupled deformation between sheet metal and bulk flexible-die, called CDSB-FEM-EFGM for short. Compared with finite element code DEFORM-2D and experiment results, the CDSB-FEM-EFGM program is feasible. This method provides a suitable numerical method to analyze sheet flexible-die forming.