金属体积成形过程有限元模拟中六面体网格重划技术的研究

针对金属体积成形过程有限元模拟中的网格重划问题,提出了基于边界构形的有限元网格重划技术,并对其中的一系列技术处理进行了详尽的讨论。将该技术应用于矩形块体镦粗过程的有限元模拟中,较好地解决了六面体网格重划问题。     

六面体单元体积坐标方法

基于二维问题四边形单元面积坐标法的成功思路,建立了三维六面体单元体积坐标的系统方法,包括:1)六面体单元特征参数的定义及单元退化模式研究;2)六面体单元体积坐标定义;3)六面体单元的体积坐标与直角坐标、等参坐标之间的关系;4)六面体体积坐标的微分公式。可以看到,六面体体积坐标保持了局部自然坐标的优点,并且与直角坐标始终保持线性关系。它为构造对网格畸变不敏感的新型六面体有限元模型提供了新工具。     

金属体积塑性成形过程数值模拟技术与仿真系统

介绍了金属体积塑性成形过程数值模拟方法、关键应用技术及其仿真系统的构成和国内外相关软件系统,对二维、三维有限元网格自动生成技术进行了较为详细的论述,综述了金属塑性成形过程优化设计方法、有限体积法以及无网格方法的国内外现状.最后给出了目前存在的问题及其将来应努力的方向.     

金属体积塑性成形过程数值模拟技术与仿真系统

介绍了金属体积塑性成形过程数值模拟方法、关键应用技术及其仿真系统的构成和国内外相关软件系统,对二维、三维有限元网格自动生成技术进行了较为详细的论述,综述了金属塑性成形过程优化设计方法、有限体积法以及无网格方法的国内外现状.最后给出了目前存在的问题及其将来应努力的方向.     

金属塑性成形三维有限元模拟软件3D - PFS的开发

金属塑性成形过程的三维有限元模拟仿真是否有效的关键在于快速适用的算法和有效的模拟系统.介绍了自主开发的三维刚塑性/刚粘塑性有限元模拟分析软件3D-PFs的组成及关键技术问题的处理,并给出了计算实例.结果表明:利用该系统可实现对体积和板料成形过程的模拟分析,获得成形过程中材料在模腔中的流动情况及成形规律,该系统是研究金属塑性成形的有效工具.     

有限元网格对RTM充模模拟的影响

本工作基于有限元控制体积法编写了模拟程序,研究了节点数量、网格密度对模拟过程的影响.以带圆孔的长方形为例,模拟比较了不同网格密度和注入口位置对充模时间、流动前沿以及干点形成区域的影响.结果表明,节点数量增加到一定程度时,只延长计算时间,对充模时间影响很小;网格疏密分布影响流动前沿的位置,根据流动前沿的形状可以确定排气口的位置和数量.     

面向叶片精锻过程的三维有限元模拟

对刚粘塑性有限元用于模拟分析叶片精锻过程的基本原理进行了论述 ;对模拟中需解决的关键问题提出了相应的算法和处理技术 ;开发了考虑工模具间的摩擦的三维刚粘塑性有限元模拟分析系统 .采用该系统 ,对航空发动机压气机简单叶片和带阻尼台叶片精锻过程进行了三维有限元模拟分析 .模拟过程中对榫头和叶身过渡处采用圆角连接 ,改善了金属的流动性和充填性 ,使叶片锻造三维有限元模拟的建模与分析更接近于实际过程 .结果表明 :采用作者所提出的基于边界构形的网格重划方法 -内缩法 ,进行畸变网格的重划是可行的 ;采用作者所提出的动态边界条件的处理方法以避免模具死锁问题是有效的 ;所开发的软件系统是可靠的 .     

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.     

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。     

三维曲面件柔性轧制成形有限元建模研究

利用柔性可弯辊轧制成形三维曲面件是一种新的板料成形方法,该文介绍了柔性轧制成形原理,基于离散化思想建立了刚性短辊按一定曲线排列的工作辊模型,解决了整体工作辊绕自身弯曲轴线无法转动的问题。给出了单元类型、网格划分技术、接触条件设置等关键问题的选择方法,利用建立的有限元模型模拟了凸曲面件的成形,模拟结果与理论分析和成形实验结果一致。     

An edge-based smoothed tetrahedron finite element method (ES-T-FEM) for 3D static and dynamic problems

Strain smoothing operation has been recently adopted to soften the stiffness of the model created using tetrahedron mesh, such as the Face-based Smoothed Finite Element Method (FS-FEM), with the aim to improve solution accuracy and the applicability of low order tetrahedral elements. In this paper, a new method with strain smoothing operation based on the edge of four-node tetrahedron mesh is proposed, and the edge-based smoothing domain of tetrahedron mesh is serving as the assembly unit for computing the 3D stiffness matrix. Numerical results demonstrate that the proposed method possesses a close-to-exact stiffness of the continuous system and gives better results than both the FEM and FS-FEM using tetrahedron mesh or even the FEM using hexahedral mesh in the static and dynamic analysis. In addition, a novel domain-based selective scheme is proposed leading to a combined ES-T-/NS-FEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The proposed method is an innovative and unique numerical method with its distinct features, which possesses strong potentials in the successful applications for static and dynamics problems.     

Adaptive generation of hexahedral element meshes for finite element analysis of metal plastic forming process

A method for the adaptive generation of hexahedral element mesh based on the geometric features of solid model is proposed. The first step is to construct the refinement information fields of source points and the corresponding ones of elements according to the surface curvature of the analyzed solid model. A thickness refinement criterion is then used to construct the thickness-based refinement information field of elements from digital topology. The second step is to generate a core mesh through removing all the undesired elements using even and odd parity rules. Then the core mesh is magnified in an inside–out manner method through a surface node projection process using the closest position approach. Finally, in order to match the mesh to the characteristic boundary of the solid model, a threading method is proposed and applied. The present method was applied in the mesh construction of different engineering problems. The resulting meshes are well-shaped and capture all the geometric features of the original solid models.     

A new automatic hexahedral mesher based on cutting

A new method is presented leading to a 20‐node brick element mesh for an arbitrary structure based on a triangulation of the structure's surface. Starting from a hexahedral master mesh encompassing the structure, the elements which are intersected by the triangulation are determined, cut and remeshed. The resulting hexahedral mesh can be tied to the underlying elements by multiple point constraints or can be continued throughout the complete structure leading to a pure 20‐node brick mesh. Several examples show the effectiveness of the method. Copyright © 2001 John Wiley & Sons, Ltd.     

Fully‐automated hex‐dominant mesh generation with directionality control via packing rectangular solid cells

A new fully automatic hex‐dominant mesh generation technique of an arbitrary 3D geometric domain is presented herein. The proposed method generates a high‐quality hex‐dominant mesh by: (1) controlling the directionality of the output hex‐dominant mesh; and (2) avoiding ill‐shaped elements induced by nodes located too closely to each other. The proposed method takes a 3D geometric domain as input and creates a hex‐dominant mesh consisting mostly of hexahedral elements, with additional prism and tetrahedral elements. Rectangular solid cells are packed on the boundary of and inside the input domain to obtain ideal node locations for a hex‐dominant mesh. Each cell has a potential energy field that mimics a body‐centred cubic (BCC) structure (seen in natural substances such as NaCl) and the cells are moved to stable positions by a physically based simulation. The simulation mimics the formation of a crystal pattern so that the centres of the cells provide ideal node locations for a hex‐dominant mesh. Via the advancing front method, the centres of the packed cells are then connected to form a tetrahedral mesh, and this is converted to a hex‐dominant mesh by merging some of the tetrahedrons. Copyright © 2003 John Wiley & Sons, Ltd.     

A close look at valences in hexahedral element meshes

This paper discusses using valences in objective functions for topological modification of 3D hexahedral meshes. For topological optimization of 2D quadrilateral meshes, node valence (i.e. number of element edges attached to each node) is used to maximize the number of regular nodes (i.e. nodes with four attached edges). Difficulties in developing 3D hexahedral local topology modifications have limited the success of hexahedral topology optimization, although published literature suggests using an object function based on node valence. However, in this paper, we show that node valence is not a consistent measure of good hexahedral element topology, and objective functions based on node valence can lead to element topology, which will only admit concave element shapes. Instead, we propose that objective functions based on edge valence (i.e. number of quadrilateral faces attached to each element edge) will provide a consistent measure of element topology. Copyright © 2010 John Wiley & Sons, Ltd.     

Efficient ALE mesh management for 3D quasi‐Eulerian problems

In computational solid mechanics, the ALE formalism can be very useful to reduce the size of finite element models of continuous forming operations such as roll forming. The mesh of these ALE models is said to be quasi‐Eulerian because the nodes remain almost fixed—or almost Eulerian—in the main process direction, although they are required to move in the orthogonal plane in order to follow the lateral displacements of the solid. This paper extensively presents a complete node relocation procedure dedicated to such ALE models. The discussion focusses on quadrangular and hexahedral meshes with local refinements. The main concern of this work is the preservation of the geometrical features and the shape of the free boundaries of the mesh. With this aim in view, each type of nodes (corner, edge, surface and volume) is treated sequentially with dedicated algorithms. A special care is given to highly curved 3D surfaces for which a CPU‐efficient smoothing technique is proposed. This new method relies on a spline surface reconstruction, on a very fast weighted Laplacian smoother with original weights and on a robust reprojection algorithm. The overall consistency of this mesh management procedure is finally demonstrated in two numerical applications. The first one is a 2D ALE simulation of a drawbead, which provides similar results to an equivalent Lagrangian model yet is much faster. The second application is a 3D industrial ALE model of a 16‐stand roll forming line. In this case, all attempts to perform the same simulation by using the Lagrangian formalism have been unsuccessful. Copyright © 2012 John Wiley & Sons, Ltd.     

Remeshing for metal forming simulations—Part II: Three‐dimensional hexahedral mesh generation

In the present study, a hexahedral mesh generator was developed for remeshing in three‐dimensional metal forming simulations. It is based on the master grid approach and octree‐based refinement scheme to generate uniformly sized or locally refined hexahedral mesh system. In particular, for refined hexahedral mesh generation, the modified Laplacian mesh smoothing scheme mentioned in the two‐dimensional study (Part I) was used to improve the mesh quality while also minimizing the loss of element size conditions. In order to investigate the applicability and effectiveness of the developed hexahedral mesh generator, several three‐dimensional metal forming simulations were carried out using uniformly sized hexahedral mesh systems. Also, a comparative study of indentation analyses was conducted to check the computational efficiency of locally refined hexahedral mesh systems. In particular, for specification of refinement conditions, distributions of effective strain‐rate gradient and posteriori error values based on a Z² error estimator were used. From this study, it is construed that the developed hexahedral mesh generator can be effectively used for three‐dimensional metal forming simulations. Copyright © 2002 John Wiley & Sons, Ltd.     

Adaptiver 3D-Vernetzungsalgorithmus zur FEM-Analyse von Massivumformvorgängen

In the numerical simulation of bulk metal forming process by the finite element method (FEM) extremely degenerated meshes result due to high local deformation. The finite elements distort so much that they lose their regular shape. Remeshing and rezoning techniques are necessary to avoid the resulting numerical problems. For remeshing it is important to create a new mesh with regular elements, and to refine the generated grid in dependency of geometric features. An automatic remeshing-module independent of the FE-code is developed at the Institute of Metal forming and Metal forming Machine tools (IFUM). This program creates a mesh that meets all requirements of the object by combination of adaptive meshing and optimisation of the correct grid distortion. In this paper an algorithm to mesh complex 3D geometries with tetrahedron elements is introduced, by taking into account the specific of metal forming processes and their implication in FE-Analysis.     

Quality improvement methods for hexahedral element meshes adaptively generated using grid‐based algorithm

The quality of finite element meshes is one of the key factors that affects the accuracy and reliability of numerical simulation results of many science and engineering problems. In order to solve the problem wherein the surface elements of the mesh generated by the grid‐based method have poor quality, this paper studied mesh quality improvement methods, including node position smoothing and topological optimization. A curvature‐based Laplacian scheme was used for smoothing of nodes on the C‐edges, which combined the normal component with the tangential component of the Laplacian operator at the curved boundary. A projection‐based Laplacian algorithm for smoothing the remaining boundary nodes was established. The deviation of the newly smoothed node from the practical surface of the solid model was solved. A node‐ and area‐weighted combination method was proposed for smoothing of interior nodes. Five element‐inserting modes, three element‐collapsing modes and three mixed modes for topological optimization were newly established. The rules for harmonious application and conformity problem of each mode, especially the mixed mode, were provided. Finally, several examples were given to demonstrate the practicability and validity of the mesh quality improvement methods presented in this paper. Copyright © 2011 John Wiley & Sons, Ltd.