柔性压辊拉形方式及其夹钳对板材成形的影响

为提高大型板类件拉形精度,介绍了传统整体夹钳拉形机的特点,提出了新型柔性压辊拉形原理.以球形件为例,分别对两种夹钳结构的拉伸成形过程建立有限元模型,并进行数值模拟,对比分析了两种夹钳结构作用下的成形结果.研究表明:柔性压辊拉形方式所得的成形件,其应力、应变分布均匀,成形质量较整体夹钳方式明显提高;而采用传统整体夹钳所成形的部件,其局部应力集中现象相对严重.利用柔性压辊拉形理论,分别对采用平板式结构夹钳和拉延筋式结构夹钳成形球形件的过程建立有限元模型并进行模拟分析,根据板材拉形过程的流动理论,对比分析两种夹持方式下板材的流动状态.研究发现:采用拉延筋式夹钳进行拉伸成形,处于夹钳中的板材流动效果较好;而利用平板式夹钳的成形过程中,板材流动量较小.实验验证结果与模拟结果趋势一致.     

金属体积成形的无网格Galerkin模拟

为避免金属体积成形有限元法模拟中网格畸变造成网格重划和模拟精度降低,采用无网格法模拟金属体积成形.利用无网格法近似位移场,建立金属体积成形的无网格法连续性控制方程,采用罚函数法施加本征边界条件和体积不变条件,基于Markov变分原理推导了金属体积成形的无网格Galerkin求解列式.用数值计算法求解该列式,实现金属体积成形的无网格模拟.数值结果表明,无网格法能有效处理金属体积成形中出现的大变形,避免了网格畸变和重划,具有较高的模拟精度.     

基于六边界优化角度函数的多道次辊弯成形研究

目的 为了提高多道次辊弯成形中板材的成形质量、减少板材纵向弯曲缺陷的产生,提出一种基于新型六边界成形角度分配函数的多道次辊弯成形优化方法。方法 根据翼缘端部水平面投影五次曲线推导出最优辊弯成形角度公式,结合COPRA研究板件峰值纵向应变,以确定最佳成形角度分配区间;在相同条件下,利用Abaquse模拟与实验研究不同成形角度对帽形件辊弯成形纵向弯曲缺陷的影响,并分析辊弯成形工艺参数对板材辊弯过程中应力-应变的影响。结果 新型六边界成形角度分配函数的多道次辊弯成形方法可有效改善板材纵向弯曲缺陷;应力随着成形角度增量的增加而增大,等效塑性应变随成形角度和成形角度增量的增加而增加;实验与模拟结果基本吻合,验证了模拟结果的正确性。结论 优化成形角度分配函数的多道次辊弯成形方法可有效改善板材纵向弯曲缺陷,为提高辊弯工艺精度与板材质量提供一定的理论指导。     

三维稳态板轧制过程的再生核质点法模拟

介绍了用再生核质点法求解刚塑性可压缩材料体积成形的基本原理,利用罚函数满足本质边界条件,积分过程采用有限元背景网格,对边界和内部采用不同的高斯积分求解方案,采用砖形影响域的张量积核函数。模拟求解了三维稳定状态板轧制过程,并将模拟结果与文献中的实测值和刚塑性有限元求解结果进行了比较,结果吻合良好,为解决具有网格畸变问题的体积成形过程奠定基础。     

金属丝网的毛坯设计

针对工业用过滤产品--过滤杯的形状及工艺条件,建立网格模型,设置成形参数,使用dynaform软件模拟其板材拉深成形的过程,通过网格数量、形状的变化,成形极限图和厚度变化图,分析比较了金属丝网与板材的性能差别.结果表明:金属丝网没有塑性变形,只有丝网的弯曲和畸变,实际成形中存在着严格的方向性.设计出了冲压金属丝网的毛坯形状.     

金属板材成形的静力隐式有限元分析与程序设计

阐述了用于板材成形过程静力隐式数值模拟的弹塑性大变形有限元方法,基于给出的方法编制了板材成形过程数值模拟软件,并对矩形板的液压胀形进行了有限元分析,计算结果与典型的实验结果吻合很好.对球形模具拉伸成形过程进行了数值模拟,给出了计算结果.     

半球形件粘性介质压力成形的数值模拟研究

粘性压力成形技术是金属板材成形领域里新近出现的一种先进的加工工艺.对双面施放粘性介质的板材胀形进行了模拟研究,在双面施放介质的板材粘性介质胀形时,排放孔位置分布对毛坯成形过程有明显的影响.排放孔位置分布的不同造成模腔内介质的速度场不同,进而导致板材不同部位的流动速度的方向大小发生变化,最终使成形件的厚度分布不同.     

铝合金板材热塑性变形行为研究

为了研究铝合金板材的热塑性变形行为,进行了热态胀形试验,获取了不同温度及压力率下的胀形压力-高度曲线,分析了压力率对胀形高度的影响规律.基于同一压力率、不同温度下胀形压力与等效应变之间的关系,提出胀形压力关于等效应变及压力率的拟合方程,同时获得压力率和应变率之间的函数关系.试验结果表明,板材充液热成形工艺过程中,压力率对金属材料的变形行为影响显著,同时压力率能够表征材料成形过程中的变形快慢.     

板材软模成形数值模拟研究现状

分析了板材软模成形数值模拟的特点,对目前主要采用的软模成形数值模拟方法进行了阐述和评价,并对三类典型软模成形(液压成形,橡皮成形及粘性介质压力成形)过程数值模拟应用进行了综述,最后对板材软模成形数值模拟发展趋势进行了展望.     

反向压力对板材粘性介质压力胀形的影响研究

为研究带有反向压力粘性介质压力胀形过程中接触条件对板材成形性的影响规律,利用DEFORMTM-2D结合韧性断裂准则对覆层板粘性介质压力胀形过程进行有限元分析.结果表明:接触表面无摩擦单纯依靠反向压力能够提高板材成形极限,随着接触表面摩擦系数增大,板材壁厚分布愈均匀,板材的破裂位置由试件顶端转移到凹模圆角处,板材成形极限显著提高.因此,在三维应力状态下有效控制板材所受法向压力和界面摩擦力可以提高板材成形性.     

A new hybrid boundary node method based on Taylor expansion and the Shepard interpolation method

A novel meshless method based on the Shepard and Taylor interpolation method (STIM) and the hybrid boundary node method (HBNM) is proposed. Based on the Shepard interpolation method and Taylor expansion, the STIM is developed to construct the shape function of the HBNM. In the STIM, the Shepard shape function is used as the basic function, which is the zero‐level shape function, and the high‐power basic functions are constructed through Taylor expansion. Four advantages of the STIM are the interpolation property, the arbitrarily high‐order consistency, the absence of inversion for the whole process of shape function construction, and the low computational expense. These properties are desirable in the implementation of meshless methods. By combining the STIM and the HBNM, a much more effective meshless method is proposed to solve the elasticity problems. Compared with the traditional HBNM, the STIM can improve accuracy because of the use of high‐power basic functions and can also improve the computational efficiency because there is no inversion for the shape function construction process. Numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

A point interpolation meshless method based on radial basis functions

A point interpolation meshless method is proposed based on combining radial and polynomial basis functions. Involvement of radial basis functions overcomes possible singularity associated with the meshless methods based on only the polynomial basis. This non‐singularity is useful in constructing well‐performed shape functions. Furthermore, the interpolation function obtained passes through all scattered points in an influence domain and thus shape functions are of delta function property. This makes the implementation of essential boundary conditions much easier than the meshless methods based on the moving least‐squares approximation. In addition, the partial derivatives of shape functions are easily obtained, thus improving computational efficiency. Examples on curve/surface fittings and solid mechanics problems show that the accuracy and convergence rate of the present method is high. Copyright © 2002 John Wiley & Sons, Ltd.     

A novel meshless approach – Local Kriging (LoKriging) method with two-dimensional structural analysis

This paper develops a novel meshless approach, called Local Kriging (LoKriging) method, which is based on the local weak form of the partial differential governing equations and employs the Kriging interpolation to construct the meshless shape functions. Since the shape functions constructed by this interpolation have the delta function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed LoKriging method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present LoKriging method. They show that the LoKriging method is highly efficient for the implementation and highly accurate for the computation.     

An improved meshless method with almost interpolation property for isotropic heat conduction problems

In the paper an improved element free Galerkin method is presented for heat conduction problems with heat generation and spatially varying conductivity. In order to improve computational efficiency of meshless method based on Galerkin weak form, the nodal influence domain of meshless method is extended to have arbitrary polygon shape. When the dimensionless size of the nodal influence domain approaches 1, the Gauss quadrature point only contributes to those nodes in whose background cell the Gauss quadrature point is located. Thus, the bandwidth of global stiff matrix decreases obviously and the node search procedure is also avoided. Moreover, the shape functions almost possess the Kronecker delta function property, and essential boundary conditions can be implemented without any difficulties. Numerical results show that arbitrary polygon shape nodal influence domain not only has high computational accuracy, but also enhances computational efficiency of meshless method greatly.     

Development of the extended parametric meshless Galerkin method to predict the crack propagation path in two-dimensional damaged structures

The parametric meshless Galerkin method (PMGM) enhances the promising features of the meshless methods by utilizing the parametric spaces and parametric mapping, and improves their efficiency from the practical viewpoints. The computation of meshless shape functions has been usually a time-consuming and complicated task in the meshless methods. In the PMGM, the meshless shape functions are mapped from the parametric space to the physical space, and therefore, the necessary computational time to generate the meshless shape functions is saved. The extended parametric meshless Galerkin method (X-PMGM) even improves the parametric property of the PMGM by incorporating the partition of unity concepts. In this paper, the development of the X-PMGM is extended by incorporating a crack-tip formulation in X-PMGM for fracture analysis and prediction of crack propagation path in the damaged structures. In this formulation, meshless shape functions are enriched by discontinuous enrichment function as well as crack-tip enrichment functions. The obtained results show that the predicted crack growth path is in good agreement with the experimental results.     

结构声辐射计算的边界无网格法

研究函数有限维逼近插值形函数的一般要求,介绍采用移动最小二乘构建无网格插值形函数的方法与步骤;通过配点法将Kirchhoff-Helmholtz边界积分方程离散为受边界条件约束的线性方程组;最后通过分块矩阵法求解约束方程组,得到离散后的声辐射传输模型数值表达式。在计算实例中,分别用边界无网格法和边界元法建立声辐射传输模型进行声场计算,计算声场值与解析值相对比的结果表明,由于边界无网格法插值形函数根据求解情况自行构建,因此更灵活,具有更高的插值和计算精度。     

Topology optimization of structures using meshless density variable approximants

This paper proposes a new structural topology optimization method using a dual‐level point‐wise density approximant and the meshless Galerkin weak‐forms, totally based on a set of arbitrarily scattered field nodes to discretize the design domain. The moving least squares (MLS) method is used to construct shape functions with compactly supported weight functions, to achieve meshless approximations of system state equations. The MLS shape function with the zero‐order consistency will degenerate to the well‐known ‘Shepard function’, while the MLS shape function with the first‐order consistency refers to the widely studied ‘MLS shape function’. The Shepard function is then applied to construct a physically meaningful dual‐level density approximant, because of its non‐negative and range‐restricted properties. First, in terms of the original set of nodal density variables, this study develops a nonlocal nodal density approximant with enhanced smoothness by incorporating the Shepard function into the problem formulation. The density at any node can be evaluated according to the density variables located inside the influence domain of the current node. Second, in the numerical implementation, we present a point‐wise density interpolant via the Shepard function method. The density of any computational point is determined by the surrounding nodal densities within the influence domain of the concerned point. According to a set of generic design variables scattered at field nodes, an alternative solid isotropic material with penalization model is thus established through the proposed dual‐level density approximant. The Lagrangian multiplier method is included to enforce the essential boundary conditions because of the lack of the Kronecker delta function property of MLS meshless shape functions. Two benchmark numerical examples are employed to demonstrate the effectiveness of the proposed method, in particular its applicability in eliminating numerical instabilities. Copyright © 2012 John Wiley & Sons, Ltd.     

A hybrid radial boundary node method based on radial basis point interpolation

The hybrid boundary node method (HBNM) retains the meshless attribute of the moving least squares (MLS) approximation and the reduced dimensionality advantages of the boundary element method. However, the HBNM inherits the deficiency of the MLS approximation, in which shape functions lack the delta function property. Thus in the HBNM, boundary conditions are implemented after they are transformed into their approximations on the boundary nodes with the MLS scheme.This paper combines the hybrid displacement variational formulation and the radial basis point interpolation to develop a direct boundary-type meshless method, the hybrid radial boundary node method (HRBNM) for two-dimensional potential problems. The HRBNM is truly meshless, i.e. absolutely no elements are required either for interpolation or for integration. The radial basis point interpolation is used to construct shape functions with delta function property. So unlike the HBNM, the HRBNM is a direct numerical method in which the basic unknown quantity is the real solution of nodal variables, and boundary conditions can be applied directly and easily, which leads to greater computational precision. Some selected numerical tests illustrate the efficiency of the method proposed.     

A priori and a posteriori analysis of the meshless Galerkin boundary node method for three-dimensional elasticity

The meshless Galerkin boundary node method is presented in this paper for boundary-only analysis of three-dimensional elasticity problems. In this method, boundary conditions can be implemented directly and easily despite the employed moving least-squares shape functions lack the delta function property, and the resulting system matrices are symmetric and positive definite. A priori error estimates and the consequent rate of convergence are presented. A posteriori error estimates are also provided. Reliable and efficient error estimators and an efficient and convergent adaptive meshless algorithm are then derived. Numerical examples showing the efficiency of the method, confirming the theoretical properties of the error estimates, and illustrating the capability of the adaptive algorithm, are reported.     

双参数地基上Kirchhoff板计算的无网格自然单元法

自然单元法是一种基于Voronoi图及Delaunay三角形剖分图,以自然邻接点插值函数为试函数的无网格数值方法。以目前该方法中自然邻接点的Laplace插值形函数为基础,求出了其一阶及二阶导函数,建立了双参数地基上Kirchhoff板弯曲挠度的自然单元法求解控制方程,并编制了相应的计算程序。通过算例分析表明了该文方法的可行性和有效性。