Research on Analysis of Tube Hydroforming with High Accuracy by Meshfree Method

本文的研究结论如下：(1)将现有的无网格技术应用于有限元分析，作为一种高精度的管件内高压成形分析方法。作为结果，提出了一种考虑几何非线性的假定应变型有限元方法，该方法假定变形梯度为常数，并在单元内取平均值。为了进一步提高计算精度，采用移动最小二乘法作为位移场的近似。这种方法使用与有限元方法相同的节点排列，并且单元也被用作积分区域。因此，任何类型的网格生成技术都是可用的。通过对线性和非线性问题的数值分析，验证了该方法的准确性。(2)为了评价管材液压成形的实用性，采用…软件对薄壁管件在轴向载荷和内压共同作用下的成形过程进行了有限元分析更多。本构模型采用粘塑性模型。轴向载荷和内压必须独立控制，以保持纵向和周向应力之比恒定。为了实现这一点，提出了一种具有两种不同加载模式的新型弧长方法。在该方法中，纵向应力与周向应力之比被控制为附加约束条件。给出了薄壁圆管在复合载荷作用下的塑性失稳条件。数值算例表明，该方法能保持应力比恒定，并能评价复合载荷作用下薄壁管材的最大加载点。(3)为了准确估计管材内高压成形的材料行为，将前人实验中观察到的静水应力敏感效应引入到最近提出的具有顶点效应的唯象塑性模型中。将该塑性模型应用到有限元方法中。为了验证该模型，将本模型预测的剪切带发展与具有晶体滑移行为的静水应力相关的晶体塑性模型的预测进行了直接比较。结果表明，本唯象模型有足够的能力再现晶体塑性预测。此外，用Marciniak，VKuczynski类方法研究了屈服对金属薄板成形极限的静压应力依赖性的影响。较少

The conclusions of this research is summarized as follows.(1) As a high accurate analysis method for tube hydroforming, the existing meshfree technique is applied to the finite element method. As results, a novel assumed strain type finite element method is proposed considering geometrical nonlinearity, in which deformation gradient is assumed to be constant and averaged within an element. For further improvement of the accuracy, the moving least-square method is adopted as the approximation of displacement field. This method uses the same nodal arrangement as in the finite element method and an element is also used as an integration domain. Therefore, any kinds of mesh generation techniques are available. The accuracy of the method is verified by illustrated numerical analyses of linear and nonlinear problem.(2) For practical evaluation of tube hydroforming, a finite element analysis of thin-walled tube which is simultaneously subjected to axial load and internal pressure is conducted … More . As for constitutive law, visco-plastic model is adopted. Axial load and internal pressure have to be independently controlled so that the ratio of longitudinal and circumferential stresses could be kept constant. To enable this, a novel arc-length method with two different loading modes is proposed. In the method, the ratio between longitudinal and circumferential stresses is controlled as an additional constraint condition. Plastic instability condition of thin-walled tube under combined loading is also presented. A numerical example demonstrates that the proposed method can keep the stress ratio constant through the analysis and evaluate the maximum loading points of thin-walled tube under combined loading.(3) For accurate estimation of material behavior for tube hydroforming, the hydrostatic stress-sensitivity effect, which has been observed in several previous experimental studies, is incorporated into a recently proposed phenomenological plasticity model with vertex-type of effect. This plasticity model is implemented into an finite element method. To test the model, shear band developments predicted by the present model are directly compared to predictions by a crystal plasticity model with hydrostatic stress-dependence of crystallographic slip behavior. It is shown that the present phenomenological model has a sufficient ability to reproduce the crystal plasticity predictions. Furthermore, an effect of the hydrostatic stress-dependence of yielding on forming limits of thin metal sheets is investigated by use of a Marciniak, VKuczynski-type approach. Less