Solve a contact problem by optimization method—to calculate the stresses for the softwheel in a harmonic gear

It is difficult to solve the contact problem by usual finite element program. In this paper, we express the contact problem as an optimization problem. In this form we do not need to know all boundary condition in advance. We only need to know the constraint conditions. This method is especially good for solving contact problem. Using this method, we calculate the stresses of the softwheel in the harmonic gear given by Shanghai Jiaotong University, and the results are in good agreement with the experimental results.     

面向对象有限元方法研究进展

综述了面向对象有限元方法的研究现状。基于国内外大量相关文献，首先评述了有限元方法的面向对象分析过程（OOA），包括对象的识别，对象属性，方法和关系的确定等等。其次涉及有限元方法的面向对象设计过程（OOD），具体讨论了人机交互，任务管理和数据管理等内容。再次讨论了有限元方法的面向对象编程过程（OOP），如编程语言的选择，面向对象有限元的应用和集成等问题。此外还延拓到面向对象方法增强有限元软件的表现，面向对象有限元的扩展等。最后展望该方法的发展动态。     

FUZZY ARITHMETIC AND SOLVING OF THE STATIC GOVERNING EQUATIONS OF FUZZY FINITE ELEMENT METHOD

The key component of finite element analysis of structures with fuzzy parameters, which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables , was the solving of the governing equations of fuzzy finite element method. Based on a given interval representation of fuzzy numbers, some arithmetic rules of fuzzy numbers and fuzzy variables were developed in terms of the properties of interval arithmetic. According to the rules and by the theory of interval finite element method, procedures for solving the static governing equations of fuzzy finite element method of structures were presented. By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers. It is shown by a numerical example that the computational burden of the presented procedures is low and easy to implement. The effectiveness and usefulness of the presented procedures are also illustrated.     

翼型跨音速流动计算和外形设计的变域变分有限元方法

在气体动力学问题研究中经常会碰到诸如激波、翼型设计等未知界面问题。未知界面的存在为该类问题的理论分析和数值求解带来了很大困难。刘高联针对未知界面问题发展了一种变域变分有限元方法,该方法将未知界面看作是一个变化区域的边界,采用变域变分将未知界面结合在变分泛函中,使其与求解流场的控制方程结合起来,从而将未知界面的求解和流场的求解完全耦合进行,因而是一种处理未知界面的独特工具,极适合于气动外形的设计求解。本文运用变域变分有限元方法对翼型跨音速流动正、反命题进行了数值研究。由于在跨音速翼型绕流中存在激波,所以为了得到压缩激波解,采用了“人工密度”办法。几个算例均得到了满意的计算结果和设计结果,证明了本文方法的有效性和优越性。     

分片试验与有限元法

提出分片试验在有限元法中有着重要的作用,它是近代有限元发展的一个主要特色。得出分片试验对位移和应变函数的要求,这些要求便是一个好的有限元法所应保证的;分析了几何方程弱形式与分片试验的关系,借此分析了杂交元、拟协调元如何满足这些要求,以及在满足这些要示的同时产生的对其他条件的影响;分析了精化直接刚度法、广义协调元和双参数法如何保证分片试验的满足;最后作为位移条件的应用例子,改进了ＢＣＩＺ元。     

Time-independent anisotropic plastic behavior by mechanical subelement models

The paper describes a procedure for modelling the anisotropic elastic-plastic behavior of metals in plane stress state by the mechanical sub-layer model. In this model the stress-strain curves along the longitudinal and transverse directions are represented by short smooth segments which are considered as piecewise linear for simplicity. The model is incorporated in a finite element analysis program which is based on the assumed stress hybrid element and the viscoplasticity theory.     

不可压缩和近乎不可压缩粘弹性问题的有限单元法

本文首先从Herrmann泛函出发,导出了不可压缩和近乎不可压缩粘弹性问题的新的本构关系,然后根据虚功原理建立了相应的有限元公式。最后编制了平面问题的有限元分析程序VFAPINP,并计算了实例。计算结果表明所介绍的分析方法和计算程序解决了泊松比趋近或等于0.5时粘弹性应力分析问题,特别适用于固体推进剂的应力分析。     

非线性随机过程的有限元分析

本文根据实际复杂工程结构独立随机变量多，计算工作量大的特点，提出了用广义随机变量替代一般的独立随机变量以减少基本随机变量的数目，用响应曲面法替代敏度法或摄动法以提高计算效率。算例证明，以上措施取得了良好的效果，有助于非线性随机有限元法在实际工程结构可靠性分析中的应用。     

加肋开孔柱壳混合有限条——有限元屈曲分析

本文提出了一种分析环加肋开孔柱壳屈曲问题的混合有限条──有限元法。环加肋柱壳作为一个构造上的正交各向异性壳处理，柱壳非开孔区采用有限条元离散，开孔区采用有限单元离散。在有限条元与有限单元交界面上，根据位移协调条件建立条元和单元的耦合关系，并据此构造一种特殊的过渡单元、联接条元和单元，进行整体分析。算例表明，这一方法对开孔柱壳屈曲问题的分折十分有效。     

A modification of Taylor-Galerkin Finite Element Method and its application

Two basic hypothesises of Taylor-Galerkin Finite Element Method are studied in this paper.One of them which is unreasonable is redefined.The only hypothesis becomes the standpoint of Generalized Finite Element.We use this idea to analysis stream function-vorticity equations with Modified Taylor-Galerkin Finite Element Method,and give the two-step solving method,which makes the solving process more reasonable than ever before.Several computational examples reveal that the results of this new method are satisfied.     

电磁对偶有限元及在波导计算中的应用

力学中的Hamilton体系采用对偶变量描述问题。电磁场采用电场和磁场两类变量描述问题。将力学中的Hamilton体系引入到电磁场问题中,电场变量和磁场变量构成对偶变量,把频域电磁场的基本方程导向对偶方程形式,建立电磁场有限元所需的对偶变量变分原理,由此推导出电磁对偶有限元。将电磁对偶有限元应用于电磁波导计算中,可确定电磁波导的传播常数。文中给出了用电磁对偶有限元方法,计算矩形波导不同模式对应的传播常数的数值计算结果。     

改进的随机有限元法

本文以有限元方法为基础,导出了结构荷载效应特征函数算式。由此,可确定结构荷载效应分布概型及其数字特征。     

Nonlinear Vibration of Plane Structures by Finite Element and Incremental Harmonic Balance Method

A nonlinear steady state vibration analysis of a wide class of planestructures is analyzed. Both the finite element method and incrementalharmonic balance method are used. The usual beam element is adopted inwhich the nonlinear effect arising from longitudinal stretching has beentaken into account. Based on the geometric nonlinear finite elementanalysis, the nonlinear dynamic equations including quadratic and cubicnonlinearities are derived. These equations are solved by theincremental harmonic balance (IHB) method. To show the effectiveness andversatility of this method, some typical examples for a wide variety ofvibration problems including fundamental resonance, super- andsub-harmonic resonance, and combination resonance of plane structuressuch as beams, shallow arches and frames are computed. Most of theseexamples have not been studied by other researchers before. Comparisonwith previous results are also made.     

Sound Radiated in a Cavity by a Vibrating Plate: Comparison between the Results of a Finite Element Method (FEMAK) and a Boundary Element Method (NoVAlea2D)

The coupling between a cavity and a vibrating plate is written as a strong coupling where both the continuity of stresses and particle velocities at the interface are taken into account. A FEM analysis reveals an important coupling between the first mode of the plate and the cavity. The pressure distribution in the cavity shows a strong quarter of a wave length pattern indicating the influence of the first Dirichlet mode in the cavity. The vibrating plate is then excited by a turbulent flow modelled by its spectral density using the Corcos model. A comparison is made between the results obtained from a FEM and a BEM formulation. Good agreements are observed concerning the plate displacements. The comparison of the cavity sound pressure levels is less good. This revised version was published online in July 2006 with corrections to the Cover Date.     

流体饱和两相多孔介质拟静态问题的有限元解法

给出基于混合物理论的流体饱和两相多孔介质模型,该模型由一可变形固体 一流体相组成。采用Ｇａｌｅｒｋｉｎ加权残值法导出求解拟静态问题的有限元公式,并编制了二维有限元程序。用程序分析了一维和二维问题,得到合理的结果。     

伽辽金有限元素法对旋翼气弹稳定性的应用

采用伽辽金加权余数有限元素法发展了一种悬停状态下无铰旋翼桨叶气弹稳定性的分析方法。分析模型包括预锥角、下垂角、预掠角、总距角、桨根预安装角、桨叶预扭角、变距轴偏置、根部外伸量和操纵线系刚度等结构参数，对无铰旋翼桨叶气弹稳定性研究有普遍适用意义。试验证明该理论可行并能用于研究无铰旋翼结构参数对桨叶气弹稳定性的影响，也能用于直升机旋翼的型号设计。     

瞬态耦合热弹塑性接触有限元分析方法

在弹性接触问题有限元混合法的基础上,把材料非线性和表面非线性两种迭代过程耦合,在瞬态温度场分析中将伽辽金法和向后差分法结合,并用混合法进行热接触迭代,把瞬态温度场分析和弹塑性接触分析耦合。提出了一种瞬态耦合热弹塑性接触有限元分析方法,并已成功地用于核容器的密封分析。     

The Space-Time Finite Element Method for Parabolic Problems

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｅｑｕａｔｉｏｎｓｗｅｃｏｎｓｉｄｅｒｅｄａｒｅａｓｆｏｌｌｏｗｓｕｔ-Δｕ =ｆ(ｕ) ,　　Ω× [0 ,Ｔ] ,ｕ｜ Ω =0 ,　　　　　 Ω× [0 ,Ｔ] ,ｕ( · ,0 ) =ｕ0 ,Ω ,( 1 )ｗｈｅｒｅΩ ∈Ｒ2 ,ｔｈｅｆｕｎｃｔｉｏｎｆ(ｕ)ｓａｔｉｓｆｉｅｓ｜ｆ(ｕ)｜≤ｃ｜ｕ｜ ,　　 ｕ∈Ｃ(Ω) . ( 2 )Ａｎｄｆ(ｕ)ｉｓＬｉｐｓｃｈｉｔｚｃｏｎｔｉｎｕｏｕｓ,ｉ.ｅ.ｉｔｓａｔｉｓｆｉｅｓ｜ｆ(ｕ) -ｆ(ｖ) ｜≤Ｌ｜ｕ-ｖ｜ ,　　 ｕ ,ｖ∈Ｃ(Ω) ,( 3 )ｗｈｅｒｅＬｉｓＬｉｐｓｃｈｉｔｚｃｏｎｓｔａ…     

螺旋式输液管道振动的有限元法分析

本文采用有限元法分析螺旋式输液管道流固耦合振动。基于哈密顿变分式推导了单元质量矩阵、刚度矩阵及科里奥利力引起的阻尼矩阵,讨论了不同的流体速度、边界条件及螺距角对输液管固有频率的影响。文内还提出用于非经典非对称阻尼系统的双边里兹向量方法,并给出该方法与HQR法在计算精度与计算时间上的比较。     

液体三维晃动特征问题的有限元数值计算方法

本文采用有限元方法数值求解任意刚性容器内液体三维晃动的固有频率和模态。通过建立液体晃动特征问题的泛函极值原理，编制了四面体等参单元有限元程序，计算了平放圆柱腔内三维液体晃动的特征频率，并将矩形容器、球腔、带“十”字隔板球形容器内的液体三维晃动计算结果与解析解、实验结果和二维有限元数值解进行了比较，程序的正确性得到了验证。