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中文摘要：
采用刚塑性材料假设，建立了刚塑性无网格伽辽金方法。利用变换法施加本质边界条件；采用反正切摩擦模型描述摩擦力边界，在局部坐标系下施加摩擦力边界条件；采用Newton-Raphson迭代方法求解刚度方程。对于挤压过程而言，当高径比较大时，可被近似为稳态流动。由于口模内速度变化梯度较大，采用最小二乘近似节点控制方法来控制近似效果。根据建立的刚塑性无网格伽辽金方法对正向、反向和复合挤压过程等进行了稳态分析，并与刚塑性有限元软件Deform模拟结果进行了相应的比较，验证了无网格伽辽金方法分析结果的正确性。
英文摘要：
Based on the hypothesis of the rigid-plastic material, the rigid-plastic meshless Galerkin method is developed. The transformation method is used to impose the essential boundary condition. The frictional boundary condition is described by using the arctangent frictional model and is imposed under the local coordinate system in order to deal with the compound boundary condition simultaneously. The Newton-Raphson iteration method is used to solve the stiffness matrix equation. The extrusion process of billets with high ratio of height to radius can be considered to be a steady-state process. Since the gradient of the velocity is high in the mould, the control method of simulation points is applied in the least square approximation The typical extrusion processes are analyzed by using the rigid-plastic meshless Galerkin method and the effectiveness of the method is demonstrated by the comparisons with the results by using the rigid-plastic finite element method.
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