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.     

板料成形数值模拟有限元求解算法

正确选用有限元求解算法是成形模拟成功的关键技术之一。阐述了板料成形数值模拟的4种有限元求解算法,即静力隐式算法、动力显式算法、静力显式算法和一步成形法,并对这4种算法进行了论述和比较,介绍了其在实际中的应用,探讨了在板料成形模拟中如何选择有限元算法进行可靠、高效的有限元分析。     

弹塑性隐式阻尼迭代法

作者给出了联立求解平衡方程、屈服条件和塑性流动方程的弱解形式, 同时提出了两种位移增量迭代算法:一是以应变增量和塑性因子为独立基本未知量的联立求解迭代算法;二是以应变增量为独立基本未知量的数值求解方法。为了避免弹塑性刚度矩阵的奇异性, 改善迭代收敛速度, 针对上述两种迭代算法本文提出了隐式阻尼迭代法, 并编写了相应脚本文件和计算流程, 并基于有限元程序自动生成系统(FEPG)生成了求解弹塑性问题的有限元源程序。最后, 通过算例验证了所提出的迭代法和计算程序的可靠性和有效性。     

一种适用于率相关晶体塑性模型的准隐式积分算法

参考经典的切线系数法,采用向前梯度法对修正的超弹性晶体塑性模型进行本构方程积分,提出了一种新的准隐式积分算法。该算法采用基于中间构型的超弹性晶体塑性模型,无需更新晶粒取向相关的状态变量;采用修正的超弹性框架,无需进行由Green-Naghdi材料共旋引起的旋转变换。这种准隐式积分算法兼有超弹性模型和切线系数法的优点。通...     

板料V形弯曲回弹的动力烛式有限元分析

板料成形后的回弹对精度影响较大，在数值模拟时对回弹进行精确预测显得非常重要。基于连续介质力学及有限变形理论，建立了适合于三给板料成形分析的显式算法的有限元数学模型，采取集中质量矩阵，用动力显式积分的方法，使位移计算显式化，避免了由材料、几何、边界条件等高度非线性因素引起的计算收敛问题。根据该模型开发了动力显式算法的板料成形过程模拟的有限元分析程序DESSFORM3D，应用该软件模拟了包括回弹在内的整个板料V形弯曲的成形过程。通过3个不同凸模行程时计算与实验的板料几何形状对比以及计算结果与实验结果对比，验证了软件计算结果的准确性。     

有限元仿真技术在板材成形中的应用

有限元仿真技术具有很强的经济性和柔性,已广泛应用于汽车钢铁工业领域。文中论述了板材成形有限元仿真分析的关键技术及其研究进展,并采用动力显式有限元软件LS-DYNA对轻型车侧围后外板零件冲压成形过程进行了仿真计算,分析了变形过程的金属流动规律。     

向量式有限元在索穹顶静力分析中的应用

索穹顶结构是一种由预应力拉索与竖杆组成的高效柔性空间结构,易发生较大位移,拉索可能出现松弛现象。该文采用向量式有限元进行了索穹顶的静力分析。向量式有限元是一种向量力学与数值计算相结合的分析方法,不同于传统分析力学方法和其他数值计算方法。向量式有限元基于运动方程求解,不需求解非线性方程组及刚度矩阵,尤其适合于发生刚体位移和几何大变形的结构或机构求解。该文首先介绍了向量式有限元的基本原理,推导了预应力索单元的求解公式,最后采用自编向量式有限元程序,分析了一个单摆模型和一个索穹顶结构模型。结果表明：向量式有限元应用于索穹顶静力分析是可行而且可靠的,在传统有限元计算难以收敛的情况下仍然可以对结构进行精确的非线性分析,为索穹顶的非线性分析提供了一种新的方法和手段。     

环件冷轧过程弹塑性动力显式算法有限元模拟

基于弹塑性变形理论,通过虚功率原理建立环件冷轧过程有限元方程,并采用对时间的中心差分格式进行求解。在进行弹塑性应力分析时,本文引入径向回映算法,并分别给出了弹塑性加载和弹性回复时的应力计算列式。开发了环件冷轧有限元模拟软件NHRing,并对矩形截面环件开式冷轧过程进行了分析计算。计算结果表明,随着轧制的进行,环件中的应变分布趋于均匀,而环件截面中心部位由于锻不透将导致端面产生“鱼尾”现象,这与实际环轧生产基本一致。     

板料V形弯曲回弹的动力显式有限元分析

板料成形后的回弹对精度影响较大,在数值模拟时对回弹进行精确预测显得非常重要.基于连续介质力学及有限变形理论,建立了适合于三维板料成形分析的显式算法的有限元数学模型,采取集中质量矩阵,用动力显式积分的方法,使位移计算显式化,避免了由材料、几何、边界条件等高度非线性因素引起的计算收敛问题.根据该模型开发了动力显式算法的板料成形过程模拟的有限元分析程序DESSFORM3D,应用该软件模拟了包括回弹在内的整个板料V形弯曲的成形过程.通过3个不同凸模行程时计算与实验的板料几何形状对比以及计算结果与实验结果对比,验证了软件计算结果的准确性.     

LYl2半球形件拉深成形过程的动力显式有限元模拟

基于连续介质力学及有限变形理论,建立了用于三维板料成形过程模拟的有限元模型,开发了动力显式算法的板料成形过程模拟的有限元分析程序DESSFORMM3D.最后,用笔者新开发的动力显式弹粘塑性有限元程序对不同压边情况下半球形件的拉深过程进行分析,并把数值结果与实验进行对比,验证了软件的计算结果.     

Efficient implicit finite element analysis of sheet forming processes

The computation time for implicit finite element analyses tends to increase disproportionally with increasing problem size. This is due to the repeated solution of linear sets of equations, if direct solvers are used. By using iterative linear equation solvers the total analysis time can be reduced for large systems. For plate or shell element models, however, the condition of the matrix is so ill that iterative solvers do not reach the huge time‐savings that are realized with solid elements. By introducing inertial effects into the implicit finite element code the condition number can be improved and iterative solvers perform much better. An additional advantage is that the inertial effects stabilize the Newton–Raphson iterations. This also applies to quasi‐static processes, for which the inertial effects finally do not affect the results. The presented method can readily be implemented in existing implicit finite element codes. Industrial size deep drawing simulations are executed to investigate the performance of the recommended strategy. It is concluded that the computation time is decreased by a factor of 5 to 10. Copyright © 2003 John Wiley & Sons, Ltd.     

A finite element model for thermomechanical analysis of sheet metal forming

A thermal model based on explicit time integration is developed and implemented into the explicit finite element code DYNA3D to model simultaneous forming and quenching of thin‐walled structures. A staggered approach is used for coupling the thermal and mechanical analysis, wherein each analysis is performed with different time step sizes. The implementation includes a thermal shell element with linear temperature approximation in the plane and quadratic in the thickness direction, and contact heat transfer. The material behaviour is described by a temperature‐dependent elastic–plastic model with a non‐linear isotropic hardening law. Transformation plasticity is included in the model. Examples are presented to validate and evaluate the proposed model. The model is evaluated by comparison with a one‐sided forming and quenching experiment. Copyright © 2004 John Wiley & Sons, Ltd.     

Stabilized finite element method for viscoplastic flow: formulation with state variable evolution

A stabilized, mixed finite element formulation for modelling viscoplastic flow, which can be used to model approximately steady‐state metal‐forming processes, is presented. The mixed formulation is expressed in terms of the velocity, pressure and state variable fields, where the state variable is used to describe the evolution of the material's resistance to plastic flow. The resulting system of equations has two sources of well‐known instabilities, one due to the incompressibility constraint and one due to the convection‐type state variable equation. Both of these instabilities are handled by adding mesh‐dependent stabilization terms, which are functions of the Euler–Lagrange equations, to the usual Galerkin method. Linearization of the weak form is derived to enable a Newton–Raphson implementation into an object‐oriented finite element framework. A progressive solution strategy is used for improving convergence for highly non‐linear material behaviour, typical for metals. Numerical experiments using the stabilization method with hierarchic shape functions for the velocity, pressure and state variable fields in viscoplastic flow and metal‐forming problems show that the stabilized finite element method is effective and efficient for non‐linear steady forming problems. Finally, the results are discussed and conclusions are inferred. Copyright © 2002 John Wiley & Sons, Ltd.     

基于参数变分原理的含夹杂Voronoi单元法及非均质材料弹塑性计算

含夹杂Voronoi单元通过在基体单元中引入一任意夹杂, 可以更好地反映非均质材料中微结构特性。基于参数势能和余能原理, 推导了无夹杂和含夹杂Voronoi单元有限元列式, 并在此基础上形成二次规划求解模型。将含夹杂Voronoi单元应用于非均质材料宏观弹塑性性能预测计算中, 分析了非均质材料中夹杂对其宏观等效弹塑性力学性能的影响。数值结果与其它方法所得结果的比较证明了本文中所给出模型的正确性和工程可适用性。      

A least‐squares coupling method between a finite element code and a discrete element code

This paper presents a coupling method between a discrete element code CeaMka3D and a finite element code Sem. The coupling is based on a least‐squares method, which adds terms of forces to finite element code and imposes the velocity at coupling particles. For each coupling face, a small linear system with a constant matrix is solved. This method remains conservative in energy and shows good results in applications. Copyright © 2014 John Wiley & Sons, Ltd.     

An immersed finite element method with integral equation correction

We propose a robust immersed finite element method in which an integral equation formulation is used to enforce essential boundary conditions. The solution of a boundary value problem is expressed as the superposition of a finite element solution and an integral equation solution. For computing the finite element solution, the physical domain is embedded into a slightly larger Cartesian (box‐shaped) domain and is discretized using a block‐structured mesh. The defect in the essential boundary conditions, which occurs along the physical domain boundaries, is subsequently corrected with an integral equation method. In order to facilitate the mapping between the finite element and integral equation solutions, the physical domain boundary is represented with a signed distance function on the block‐structured mesh. As a result, only a boundary mesh of the physical domain is necessary and no domain mesh needs to be generated, except for the non‐boundary‐conforming block‐structured mesh. The overall approach is first presented for the Poisson equation and then generalized to incompressible viscous flow equations. As an example of fluid–structure coupling, the settling of a heavy rigid particle in a closed tank is considered. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimal process design in non-isothermal,non-steady metal forming by the finite element method

A new approach to process optimal design in non-isothermal, non-steady-state metal forming is presented. In this approach, the optimal design problem is formulated on the basis of the integrated thermo-mechanical finite element process model so as to cover diverse objective functions and design variables, and a derivative-based approach is adopted for conducting optimization. The process model, the formulation for process optimal design, and the schemes for the evaluation of the design sensitivity, and an iterative procedure for optimization are described in detail. The validity of the schemes for the evaluation of the design sensitivity is examined by performing a series of numerical tests. The capability of the proposed approach to deal with diverse process parameters and objective functions is demonstrated through applications to some selected process design problems. © 1998 John Wiley & Sons, Ltd.     

The inside–outside contact search algorithm for finite element analysis

A new contact search algorithm (Inside–Outside Algorithm) for the sheet forming simulation has been developed and implemented in the dynamic explicit FE code: ‘DYNAMIC’. The inside–outside algorithm is derived based on the feature of the inside–outside status of a nodal ‘mesh normal vector’ in respect to a surface segment for the judgment of the contact of FE nodes with the tool surface. This new algorithm includes local search, local track and penetration calculation processes. Almost no additional CPU time is required for the local search process, because the calculations for both global and local search are combined. Moreover, the problems of conventional contact searching algorithms, such as iterations for local search and the deadzone problem, are resolved. Therefore, the quick, robust contact searching and accurate evaluation of penetration have been achieved. The numerical results show that the new contact searching algorithm is more cost effective and robust than conventional ones. © 1997 John Wiley & Sons, Ltd.