【作者】 吴欣；

【导师】 赵国群；

【作者基本信息】 山东大学 ， 材料加工工程， 2006， 博士

【摘要】 金属塑性成形技术在金属零件的制造过程中起着十分重要的作用。它不仅具有生产效率高、产品质量稳定、原材料消耗少的优点，而且还可以有效地改善工件的组织性能。随着计算机技术的发展和数值计算方法的日益完善，有限元方法在工程实际中得到了广泛的应用。但是，当工件变形到一定程度时，有限元网格将产生畸变现象，此时，这种以单元作为基本概念的有限元方法面临着一些难以处理的问题。无网格方法基于离散节点的近似，避免了有限元方法对于网格的依赖，在涉及到网格畸变的大变形问题分析中具有一定的优势，并且在数据准备和后处理方面也比有限元方法灵活简单。 无网格方法作为一种较为新颖的数值方法，经过十余年的发展，已经逐渐应用于金属塑性成形过程的模拟，并且取得了一定的成果。但是对于非稳态大变形金属塑性成形问题，由于成形过程的复杂性，许多关键应用技术还有待于研究。尤其当金属流动比较剧烈或变形比较复杂时由于节点分布的非均匀性增强和变形域形状更加复杂，速度场的近似精度和变形域的积分精度会有所下降，进而导致数值模拟出现错误。因此，本文针对非稳态大变形成形过程，主要研究了基于刚(粘)塑性材料假设的无网格伽辽金方法、关键处理技术及其在金属塑性成形过程分析中的应用。 基于无网格近似方案，结合伽辽金离散方法，提出了刚(粘)塑性无网格伽辽金方法。速度场采用经过变换法修正处理的最小二乘近似和再生核质点近似或者直接采用径向基函数插值进行近似。采用反正切摩擦模型描述摩擦接触边界条件。对于模具形状任意的塑性成形过程，在局部坐标系下施加摩擦力边界条件，给出了局部坐标系和整体坐标系的变换矩阵，解决了模具形状任意的二维塑性成形过程分析中的摩擦接触边界条件施加问题。在此基础上推导建立了金属塑性成形过程无网格方法分析刚度矩阵方程。进而采用直接迭代法获得初始速度场，利用Newton-Raphson迭代方法求解刚度方程。最后给出了模拟等温塑性成形问题的分析步骤。 针对非稳态金属塑性成形过程的复杂性、数学处理上的困难性和在成形过程模拟分析模型建立以及分析程序的通用化方面存在的不足，研究了刚(粘)塑性无网格伽辽金方法应用于金属塑性成形过程分析的关键处理技术。对于任意边界形状的二维金属塑性成形过程的无网格伽辽金方法分析，建立了诸如任意形状模具描述方法、迭代收敛判据、接触脱离判断等问题的处理方法，实现了非稳态任更多还原

【Abstract】 The technology of metal forming processing plays an important role in metal part manufacturing. Its advantages are not only in its high productivity, stable quality, and low cost of raw and processed materials, but also in its characteristics of improving the microstructure performance dramatically. With the development of computer technology and computational methods, the finite element method (FEM) gained great achievement and was applied wildly in many engineering fields. Although great success in the metal forming process numerical simulation is achieved by FEM, the mesh distortion will be inevitable for the accumulation of the metal deformation. Then many difficulties will be occurred in FEM analysis for dependence of the approximation precision on the mesh. Compared with FEM, the meshless approximation based on discrete point information has advantages in the simulation of large deformation problems with mesh distortion for getting rid of the reliance on the mesh. Simultaneously, meshless method is more flexible and simpler than FEM in data prepare for the problem simulation and post-process of simulation results.The meshless method, a newly developed numerical method, was used to the simulation of metal forming process after decade’s development, and some progresses were obtained. But there are still many key techniques, which need more attention for the complexity of the metal deformation in unsteady metal forming process. Especially when the deformation is more severe or metal flow is more complex, the approximation precision of the velocity field and integration precision of deformation domain will be deteriorated for the severe un-uniformity of the metal flow and complexity of the deformation zone. Thus simulation error will be occurred. So, the study focused on the development of the rigid-visco plastic meshless Galerkin method and its key techniques for unsteady large deformation metal forming process.The meshless Galerkin method is introduced into the analysis of the metal forming processes. Under the hypothesis of the rigid-visco plastic material, a rigid-visco plastic meshless Galerkin method is developed. The velocity field is approximated by Moving Least Square (MLS) method, Reproducing Kernel Producing Method (RKPM) and Radial Basis Function (RBF) in which MLS and RKPM is modified by the transformation method in order to employ the essential boundary condition directly. An arctangent frictional model is used to describe the frictional boundary condition. For the更多还原