刚塑性无网格伽辽金方法近似方案研究

研究了最小二乘近似、再生核质点近似、径向基函数近似以及一致径向基函数近似等方案的近似特点,并将其应用于金属塑性成形过程刚塑性无网格伽辽金分析中。采用变换法修正速度场近似,采用反正切摩擦模型施加摩擦边界条件,结合金属刚塑性流动理论,建立了刚塑性无网格伽辽金方法,并分析了各近似方案在金属塑性成形过程分析中的应用特点和前景。通过典型函数近似和塑性成形过程的模拟近似,获得了关于各近似方案近似能力和在成形过程分析中应用的一些结论。

The study on the approximation methods in rigid plastic meshless Galerkin method

The characters of the Moving Least Square(MLS) approximation method,Reproducing Kennel Particle Method(RKPM),Radial Basis Function(RBF) approximation method and Consistent Radial Basis Function approximation method are studied.These meshless approximation methods are introduced into the meshless Galerkin analysis of the metal forming processes.The transformation method is used to modify velocity approximation.The arctangent frictional model is used to describe frictional boundary condition.Thus a rigid plastic meshless Galerkin method is devolved based on rigid plastic flow theory.The characters and foreground of these approximation methods are studied in the application of the rigid plastic meshless Galerkin method.Some conclusions are obtained through approximation of typical functions and simulation of typical metal forming process.