四阶特征值问题的各向异性有限元方法

本文的主要目的是讨论在各向异性网络剖分下四阶特征值问题的双三次Hernmite有限元逼近。由于该网格不同于传统有限元方法中的正则性剖分或拟一致剖分,在理论分析过程中不能直接使用Sobolev插值理论。本文将利用新的技巧,导出与传统网格剖分下相同的最优误差估计。     

飞行器RCS计算中曲面剖分技术研究与实现

飞行器RCS预估计算是隐身技术研究中的重要研究内容。论述了利用飞行器外形的特点,在满足飞行器设计误差的前提下使用平面和柱面对飞行器的整机作NURBS曲面逼近,然后用柱面和平面剖分代替曲面的剖分。实现了飞行器整机模型的指定边长的三角剖分。这种方法不同于有限元计算的网格剖分,具有网格单元与曲面曲率无关和剖分速度快等特点。     

基于映射理论的网格生成新方法及应用研究

基于映射函数理论提出二维/三维流场的网格生成新方法。针对实际应用中对场函数变密度的要求,提出可控制网格疏密度的插值公式,并以此对典型物体周围流场进行网格剖分,验证其有效性。针对圆形域(柱形域)流场网格生成质量的缺陷,提出在目标域中建立内置块的新策略,统计分析网格最小内角分布,并与原方法对比分析,以验证改进效果。运用自编程序,对具有复杂外形的空间膜结构进行流场网格剖分,并将该网格导入Ansys-CFX软件,进而数值模拟结构表面风压分布。经验证,该方法可有效地运用于流场网格剖分。     

使用多重网格算法的一种途径

采用坐标变换方法，将物理平面中任意几何区域上的非均匀网格剖分映射到计算平面中规则区域上的均匀网格剖分，这种处理使得对某些问题的多重网格算法成为方便可行，文后给出了两个算例。     

一种新型球面等积六边形网格系统生成算法

分析了构建球面等积网格系统的基本原理和常用剖分方法的特点,提出了在二十面体展开图上对顶点和面统一编码的研究思路,将两个相邻三角面合并为一个四边形并建立坐标系描述孔径为4的新型递归剖分网格,最后借助施奈德等积多面体投影将平面网格映射到球面,得到了将孔径为4的等积六边形剖分产生的球面网格系统ISEA4H-3.实验结果表明,用这种算法生成的ISEA4H-3网格的几何属性优于现有球面六边形网格,更适用于海量空间信息管理,具有较强的应用价值.     

二维任意域约束Delaunay三角化的实现

本文设计了一种逐点加入一局部换边法,提出并证明了二维约束边在约束Ｄｅｌａｕｎａｙ三角化中存在的条件,并据此用中点加点法实现了二维任意域的Ｄｅｌａｕｎａｙ三角剖分,生成的网格均符合Ｄｅｌａｕｎａｙ优化准则,网格的优化在网格生成过程中完成,算法复杂度与点数呈近似线性关系,给出了算法在平面域剖分和包含复杂断层的石油地质勘探散乱数据点集剖分的应用实例。     

大坝有限元分析应力取值的研究

提出了基于误差控制下的自适应网格的有限元应力取值标准:即给定一全局误差限作为自适应有限元网格剖分的准则,以此网格计算所得应力即为有限元应力取值。应用适用于工程计算的Z2后验误差估计方法以及h-型自适应策略,对一个典型的重力坝剖面进行了线弹性自适应有限元计算。计算结果表明:给定一个全局误差限,网格剖分调整若干次后即可满足误差要求,不会出现因角缘应力集中出现剖分不收敛的情况;存在一个全局误差限,使得当继续降低误差限时,坝踵和坝趾的角缘应力趋于稳定值。     

三维Delaunay剖分的断层直接插入算法

研究了在三维空间中进行的Delaunay四面体剖分。在讨论了四面体网格与插入的受限平面数据的各种相交构形的基础上,提出了一种断层直接插入的算法。该算法可以应用于三维数据点集的受限四面体剖分,也可以应用于不同的数据场网格之间的相交运算等问题。     

位移障碍下变分不等式问题的各向异性非协调有限元方法

本文研究位移障碍下二阶变分不等式问题在各向异性网格上的非协调有限元逼近。通过运用新的方法和技巧,得到了与正则网格剖分下相同的最优误差估计,从而扩展了有限元的应用范围。     

三维德洛内三角剖分算法探析

三维德洛内三角剖分算法是一种新颖的适用于实时有限元分析的四面体网格生成算法,该算法在并行插入与删除网格节点的前提下,能够最大限度的保证网格生成的质量和保真度。     

The green element method

This paper discusses an element-by-element approach of implementing the Boundary Element Method (BEM) which offers substantial savings in computing resource, enables handling of a wider range of problems including non-linear ones, and at the same time preserves the second-order accuracy associated with the method. Essentially, by this approach, herein called the Green Element Method (GEM), the singular integral theory of BEM is retained except that its implementation is carried out in a fashion similar to that of the Finite Element Method (FEM). Whereas the solution procedure of BEM couples the information of all nodes in the computational domain so that the global coefficient matrix is dense and full and as such difficult to invert, that of GEM, on the other hand, involves only nodes that share common elements so that the global coefficient matrix is sparse and banded and as such easy to invert. Thus, GEM has the advantage of being more computationally efficient than BEM. In addition, GEM makes the singular integral theory more flexible and versatile in the sense that GEM readily accommodates spatial variability of medium and flow parameters (e.g., flow in heterogeneous media), while other known numerical features of BEM—its second-order accuracy and ability to readily handle problems with singularities are retained by GEM. A number of schemes is incorporated into the basic Green element formulation and these schemes are examined with the goal of identifying optimum schemes of the formulation. These schemes include the use of linear and quadratic interpolation functions on triangular and rectangular elements. We found that linear elements offer acceptable accuracy and computational effort. Comparison of the modified fully implicit scheme against the generalized two-level scheme shows that the modified fully implicit scheme with weight of about 1·25 offers a marginally better approximation of the temporal derivative. The Newton–Raphson scheme is easily incoporated into GEM and provides excellent results for the time-dependent non-linear Boussinesq problem. Comparison of GEM with conventional BEM is done on various numerical examples, and it is observed that, for comparable accuracy, GEM uses less computing time. In fact, from the numerical simulations carried out, GEM uses between 15 and 45 per cent of the simulation time of BEM.     

采用广义协调条件构造具有旋转自由度的四边形膜元

本文根据广义协调的概念,通过引进单元结点刚体转角,提出两种具有平面内旋转自由度的四边形膜元。单元列式简单,是能通过任意四边形分片检验的收敛单元。数值计算表明这两种单元无论是位移还是应力都有很高的计算精度。     

具有旋转自由度的广义协调矩形膜元

本文根据广义协调的思想,在平面应力矩形单元双线性协调位移场中,引入附加广义泡状位移场,构造出一种具有平面内旋转自由度的矩形膜单元,它满足广义协调条件。数值计算结果表明,这种单元有很高的计算精度,而且计算量少,是一种能收敛于精确解的单元。     

广义协调平板型三角形壳元

本文构造了一种具有三个角点十八个自由度的平板三角形壳元GST18。其拉伸与弯曲部分分别由含旋转自由度的三角形膜元和薄板弯曲三角形元组成。广义协调方法的采用,使得该单元的收敛性得到保证。在结点上引入了平面内旋转自由度,从根本上克服了单元共面刚度矩阵出现奇异这一困难。对平面膜元采用了缩减积分方案,使该单元不会产生薄膜闭锁现象。数值算例表明,本文提出的GST18薄壳元是计算精度优于同类单元的可靠、实用的单元。     

带转角自由度的四边形六面体单元

本文提出了三个带转角自由度单元，其中一个平面四边形单元，两个空间六面体单元。对平面单元每个结点有两个线位移自由度、一个转角自由度；对空间单元，每个结点有三个线位移自由度、三个转角自由度。这些单元列式简单，其中两个无多余零能模式，数值计算表明，它们的计算精度高。     

非协调元性能分析的两个定理

在构造非协调元的过程中,必须遵守一定的构造规律。本文从基本力学观点出发,提出并证明了两个定理。定理一、如果某种类型的有限单元共有n个独立参与整体刚度运算的自由度,则该单元最多只能精确模拟n种弹性力学基本解。该定理说明了单元的精度从根本上受自身自由度限制的,并指出了现有的四边形四结点单元发展空间不大,而四边形八结点Q8单元以及三维八结点H8单元仍然具有较大的发展余地。定理二则认为四边形四结点内参型非协调元如果能够通过小片试验,则不可能在任意畸变状态下精确表示纯弯场。该定理表明了畸变问题的尝试是有限制的。以上的结论虽然是针对非协调元的构造来提出的,但从论证过程看,应对其它类型的有限单元也适用。定理一和定理二对于今后新型有限元的发展可以起到一定的指导作用。     

带转角自由度的三角形三棱柱单元

本文提出了一个带转角自由度平面三角形单元、两个带转角自由度空间三棱柱单元。对平面单元每个结点有两个线位移自由度、一个转角自由度；对空间单元每个结点有三个线位移自由度、三个转角自由度。这些单元列式简单，其中两个无多余零能模式，数值计算表明，它们的计算精度高。     

A 3‐node flat triangular shell element with corner drilling freedoms and transverse shear correction

The formulation, implementation and testing of simple, efficient and robust shell finite elements have challenged investigators over the past four decades. A new 3‐node flat triangular shell element is developed by combination of a membrane component and a plate bending component. The ANDES‐based membrane component includes rotational degrees of freedom, and the refined nonconforming element method‐based bending component involves a transverse shear correction. Numerical examples are carried out for benchmark tests. The results show that compared with some popular shell elements, the present one is simple but exhibits excellent all‐around properties (for both membrane‐and bending‐dominated situations), such as free of aspect ratio locking, passing the patch test, free of shear locking, good convergence and high suitability for thin to moderately thick plates. The developed element has already been adopted in a warpage simulation package for injection molding. Copyright © 2011 John Wiley & Sons, Ltd.     

Genetic algorithm based deformation control and clamping force optimisation of workpiece fixture system

In re-engineering mass production industry, design and production of components are frequently changed according to the customer needs within a very short span of time. This leads to rising difficulty in maintaining the accuracy of every finished component. It also induces the long setup time of the cutting tools and machine tools affecting the production rate of the components. To reduce the production time and to improve the accuracy of the finished product, proper fixture element is essential. The accuracy of the finished work-piece strongly depends on the position of the locators and clamps in the work-piece fixture system. The finite element analysis tool is well suited to predict the active and passive forces on the work piece-fixture system. The accuracy of the workpiece not only depends on the clamping force but also depends upon the locator force (reaction force). This paper presents the optimisation of the locations of active (clamp) and passive (locator/support) elements in the workpiece-fixture system using genetic algorithm (GA) with ANSYS parametric design language (APDL) of finite element analysis. Three case studies are given to illustrate the application of the proposed approach. Finally the case study results have been compared with the Li and Melkote (1999a Li, B and Melkote, SN. 1999a. An elastic contact model for the prediction of workpiece-fixture contact forces in clamping. ASME Journal of Manufacturing Science and Engineering, 121(3): 485–493.  [Google Scholar]) [Li, B. and Melkote, S.N., 1999a. An elastic contact model for the prediction of workpiece-fixture contact forces in clamping. ASME Journal of Manufacturing Science and Engineering, 121(3), 485–493] study. This presented prediction method is conceptually simple and computationally efficient.     

THE NONCONFORMING ELEMENT METHOD AND REFINED HYBRID ELEMENT METHOD FOR AXISYMMETRIC SOLID

The general approach for constituting non-conforming displacement function has been developed for axisymmetric finite element analysis and a pure non-conforming quadrilateral axisymmetric element, from a non-conforming displacement function and without any reduced integration technique, is given. Based on a proposed functional for formulating axisymmetric element and the orthogonal approach, a quadrilateral axisymmetric refined hybrid element has been presented which can be used to achieve superior performances such as higher accuracy and free from locking.