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中文摘要：
径向基函数满足δ条件，可以直接施加本质边界条件，通过耦合多项式基函数可以精确重构任意多项式。将无网格伽辽金方法引入到塑性成形过程模拟，结合刚塑性材料的假设，提出基于一致径向基函数的无网格刚塑性伽辽金方法。采用体积应变率映射法处理体积不可压缩条件；采用反正切摩擦模型在局部坐标系下施加摩擦力边界条件，实现任意边界形状的塑性成形过程模拟。对典型塑性成形过程进行无网格方法分析，并与刚塑性有限元方法及试验数据进行比较，验证了建立方法的可行性。
英文摘要：
Since the radical basis functions satisfy the kronecker δproperty, the velocity boundary condition can be employed directly. The polynomial functions can be accurately reproduced through the coupling of the polynomial functions into the radical basis function approximation. The meshless Galerldn method is introduced into the metal forming simulations. A meshless Galerkin method based on the consistent radical basis function approximation is developed under the hypothesis of the rigid plastic theory. The volume strain rate projection method is used to deal with the incompressibility constraint. An arctangent frictional model is used to impose the frictional boundary condition under the local coordinate system. In this way, the meshless simulation of the metal forming processes with arbitrarily shaped die is realized. Several typical metal forming processes are analyzed by using the method developed. The effectiveness of the method is demonstrated through the comparisons of the simulation results with those obtained by using rigid plastic FEM method and experiments data.
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