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

本研究的结论归纳如下。(1)无网格技术作为一种高精度的管材液压成形分析方法，被应用于有限元分析中。在此基础上，提出了一种新的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。为了进一步提高精度，采用移动最小二乘法作为位移场的近似。该方法使用与有限元法相同的节点布置，并且单元也用作积分域。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)为了对管材液压成形进行实用性评价，对同时承受轴向载荷和内压的薄壁管材进行了有限元分析 ...更多信息 .本构关系采用粘塑性模型。轴向载荷和内压必须独立控制，以使纵向和周向应力比保持恒定。为了实现这一点，提出了一种新的弧长方法与两种不同的加载模式。在该方法中，纵向和周向应力之间的比例作为一个附加的约束条件进行控制。给出了复合载荷作用下薄壁管塑性失稳的条件。数值算例表明，该方法通过分析可以保持应力比恒定，并确定薄壁管在组合载荷作用下的最大载荷点。(3)为了准确估计管材液压成形的材料行为，流体静力学应力敏感性效应，这已被观察到在以前的几个实验研究，被纳入最近提出的唯象塑性模型与顶点型的效果。该塑性模型被实现为有限元方法。为了测试该模型，剪切带的发展预测本模型直接比较晶体塑性模型与静水应力依赖的晶体滑移行为的预测。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，静水压力的屈服对薄金属板成形极限的依赖性的效果进行了研究通过使用Marciniak，VKuczynski型方法。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