【作者】 崔青玲；

【导师】 刘相华； 王国栋；

【作者基本信息】 东北大学 ， 材料加工工程， 2005， 博士

【摘要】 无网格方法是近年来出现的一种新的数值模拟方法，其基本特点是场函数建立在独立的节点上，节点之间无需网格联接。再生核质点法是无网格方法的一种，通过具有紧支集的核函数的积分转换得到场变量的近似。再生核的原意是函数通过积分能够再生。本文主要探讨再生核质点法在金属成形中尤其是轧制中的应用的可行性，为轧制过程的模拟提供新的研究手段。 由于无网格法的形函数不具备插值特性，近似函数不能自动满足本质边界条件，本文采用罚函数法满足边界条件，即在能量泛函表达式中添加对边界条件的惩罚项；对平面应变假设的刚塑性可压缩材料的二维轧制过程，摩擦模型采用Koboyashi模型，积分过程利用有限元背景网格，对内部积分和摩擦边界采用不同的积分方案，并利用缩减积分防止体积闭锁现象；采用影响域为矩形的张量积核函数；利用直接迭代法建立迭代过程求解非线性方程组。将所建模型用于有实验背景的轧制过程模拟，并将计算结果与刚塑性有限元的计算结果和实验数据进行对比，以验证无网格方法求解轧制过程的正确性。 在平面变形的基础上，将模型扩展至三维轧制过程，与二维类似，核函数影响域为砖形。对带外端的情形，利用在入口处节点加密的方法处理速度不连续面的奇异点。计算结果表明，带前后外端由于更接近实际轧制情况，因而与不带外端情况相比，计算精度更高。 对立轧这种典型的超高件的轧制过程，由于在轧件边部存在严重的局部变形，所以对内部的高斯积分点需采用双线性一致性条件。而如果对接触表面的高斯点也采用双线性一致性，则入口处加密的节点会对摩擦能耗率产生不良影响，数值模拟可能不稳定甚至发散，所以在接触表面的高斯积分点仅满足线性一致性条件。狗骨材形状及轧制力能参数等计算结果验证了模型的正确性。利用立轧的节点信息对狗骨材的水平轧制进行了模拟。 切分轧制中存在严重的网格畸变和金属撕裂过程，对网格畸变问题，有限元法求解需要重新划分网格，但对金属撕裂的极端变形过程，由于网格的限制有限元方法无法继续求解。而无网格方法不存在网格畸变问题，随着变形的加大可以继续求解，且轧件分开时不受网格限制。利用无网格方法对切分轧制过更多还原

【Abstract】 As a new numerical simulation method, meshless methods perform the discretization of the workpiece entirely in terms of arbitrarily placed nodes without use of an explicit mesh. Reproducing kernel particle method is one of the meshless methods. The approximation of the unknown function in a domain is accomplished by means of kernel estimates. The kernel estimate of a function is an integral transformation through a kernel function which has a compact support. The reproducing kernel is a class of operators that reproduce the function itself through integration over the domain. This dissertation focus on the validity of the application of the reproducing kernel particle method in metal forming especially in rolling process, in order to provide a new research means for rolling process simulation.The shape function of meshless methods is not an interpolation function, so the enforcement of essential boundary condition is difficult in meshless method. In this dissertation the penalty method is used to enforce the essential boundary, i.e. a penalty term is added in the energy function. For 2D rolling under the plain strain condition of compressible rigid-plastic materials, the interface friction is treated by Koboyashi model. The integration process is accomplished by using the finite element background cell, and different types of Gauss point quadrature schemes is introduced in the interior and the boundary, and the reduced integration is used to prevent the volumetric locking. The tensor product weight function which has brick influence domain is used. The nonlinear system equation is solved by the direct iterative method. The effectiveness of the proposed approach is discussed by comparing theoretical predictions with experimental data found in the literature and the rigid-plastic finite element.On the basis of the previous work in two-dimensional meshless applications, the meshless model is introduced to the three-dimensional steady state flat rolling. The velocity discontinuity at rolling entry can be successfully treated through the implementation of adding a layer of nodes. The simulation results of 3D model with rigid ends is more exact than that ones of 3D model without rigid ends due to it is more resemble to the fact.更多还原