FGM环扇形板的面内自由振动分析

假定功能梯度材料(FGM)的物性参数沿环扇形板径向按照幂律梯度变化,基于平面线弹性理论,建立了FGM环扇形板面内自由振动的运动控制微分方程。采用二维微分求积法(DQM)对FGM环扇形板面内自由振动的无量纲运动控制微分方程进行离散,数值求解了不同边界条件下FGM环扇形板面内自由振动的无量纲固有频率,同时也给出了FGM环扇形板扇形角为!/4时有限元商用软件ANSYS的部分计算结果,验证了本文方法的正确性。结果表明,在相应边界条件下,FGM环扇形板的梯度指标、内外半径比以及扇形角对无量纲固有频率均有影响,其计算结果和分析方法可供设计和研究参考。     

基于物理中面FGM板屈曲的有限元分析

基于物理中面的概念,根据最小势能原理推导了功能梯度材料FGM薄板屈曲的有限元控制方程,求得临界荷载的有限元解。利用FGM板的屈曲方程与参考均匀板的屈曲方程之间的相似性,建立了FGM板的临界荷载与参考均匀板的临界荷载之间的相似转换关系式,从而将FGM板临界荷载的计算转变为参考均匀板的临界荷载和材料不均匀系数的计算,极大地提高了计算效率,为FGM的推广起积极的推动作用。通过数值算例,将由有限元法和转换关系式得到的临界荷载进行了比较,并讨论了边界条件、荷载工况、材料组成和几何尺寸等对FGM板临界荷载的影响。     

Three-dimensional free vibration analysis of multi-directional functionally graded piezoelectric annular plates on elastic foundations via state space based differential quadrature method

The three-dimensional free vibration analysis of a multi-directional functionally graded piezoelectric(FGP) annular plate resting on two parameter(Pasternak)elastic foundations is investigated under different boundary conditions. The material properties are assumed to vary continuously along the radial and thickness directions and have exponent-law distribution. A semi-analytical approach named the state space based differential quadrature method(SSDQM) is used to provide an analytical solution along the thickness using the state space method(SSM) and an approximate solution along the radial direction using the one-dimensional differential quadrature method(DQM).The influence of the Winkler and shear stiffness of the foundation, the material property graded variations, and the circumferential wave number on the non-dimensional natural frequency of multi-directional FGP annular plates is studied.     

弹性力学平面问题的等价边界积分方程的边界轮廓法

基于边界积分方程中被积函数散度为零的特性,提出了弹性力学平面问题的等价边界积分方程的边界轮廓法,该方法无需进行数值积分,只需要计算单元两结点势函数值之差。实例计算说明,基于传统的边界积分方程的边界轮廓法所得到的面力结果是错误,而本文建立的边界轮廓法则可给出精确的结果。     

各向异性弹塑性中厚度板壳的有限元分析

本文在文献［２，３］的基础上，提出了一个解各向异性弹塑性中厚度板壳问题的有限元方法。考虑材料各向异性的特点，采用了Ｈｉｌｌ推广的Ｈｕｂｅｒ－Ｍｉｓｅｓ屈服准则；借用Ｏｗｅｎ的剪切修正系数，正确计及了叠层复合材料壳体的横向剪切效应；为了避免“自锁”现象，文中采用了９节点的Ｈｅｔｅｒｏｓｉｓ二次壳单元；特别是本文利用插值外推的思想，提出了一个带预测的弧长增量控制法，显著提高了确定变形路径的计算效率。几个数值算例表明本文给出的有限元方法对于各向异性中厚度板壳的弹塑性分析有较好的精度，尤其是对具有复杂变形路径的结构计算，收敛速度提高更快。     

Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis

Advancements in manufacturing technology, including the rapid development of additive manufacturing (AM), allow the fabrication of complex functionally graded material (FGM) sectioned beams. Portions of these beams may be made from different materials with possibly different gradients of material properties. The present work proposes models to investigate the free vibration of FGM sectioned beams based on onedimensional (1D) finite element analysis. For this purpose, a sample beam is divided into discrete elements, and the total energy stored in each element during vibration is computed by considering either the Timoshenko or Euler-Bernoulli beam theory. Then, Hamilton's principle is used to derive the equations of motion for the beam. The effects of material properties and dimensions of FGM sections on the beam's natural frequencies and their corresponding mode shapes are then investigated based on a dynamic Timoshenko model (TM). The presented model is validated by comparison with three-dimensional (3D) finite element simulations of the first three mode shapes of the beam.     

全应变梯度挠曲电纳米梁有限单元法研究

挠曲电效应是一种存在于所有电介质材料中的特殊的力电耦合效应,本质上是应变梯度与电极化之间的线性耦合。然而,应变梯度会引入位移的高阶偏量,常给挠曲电问题的理论求解带来困难。且已有研究表明应变梯度弹性项会影响纳米结构中的力电耦合响应,但是现有的挠曲电研究大多忽略了应变梯度弹性的影响。因此,本文提出了一种既考虑应变梯度弹性,又考虑挠曲电效应的有效数值方法。基于全应变梯度弹性理论,建立了包含3个独立材料尺度参数的纳米欧拉梁的理论模型和有限元模型,提出了满足C₂弱连续的两节点六自由度单元。基于本文的有限单元法,以简支欧拉梁为例,通过分析讨论挠度、电势和能量效率,得到了挠曲电效应和应变梯度弹性项对梁的力电响应的影响。结果表明,挠曲电效应存在尺寸依赖性,且应变梯度弹性项在纳米电介质结构的挠曲电研究中的影响不可忽略。     

有限厚双边U型切口板的三维弹塑性有限元分析

针对单向拉伸载荷作用下的有限厚双边 U型切口板 ,本文对其切口根部的三维效应进行了详细的三维弹塑性大变形有限元分析 ,得到了不同于平面切口问题的新结果 :( 1 )在线弹性阶段 ,三维切口根部的应力集中因子 Kt高于二维情形 ,且 Kt在板厚 ( B)约为 8倍切口根部半径 (ρ)时达到峰值 ;进入塑性后 ,切口根部的 Kt随载荷水平的增加逐渐下降 ,并介于平面应力和平面应变情形之间 ;( 2 )切口前缘等效应变εe的最大值出现在约束最高的中面 ,且可比约束最低的自由表面处的应变值高一倍 ;( 3)薄板中 ,塑性区尺寸 xp 的最大值不是出现在约束较低的自由表面 ,而是出现在约束较高的中面 ,但随 B/ρ的增大逐渐向自由表面外推 ;( 4 )面内应力比 Tx在切口根部塑性区内的分布对板厚和载荷水平不敏感 ,可以用 Hill的滑移线解很好地近似。另外 ,对三维影响区内一些重要的三维约束参量进行了详细分析 ,总结了它们的三维分布规律。     

基于等几何有限元法的功能梯度微板热力耦合屈曲预测

基于修正偶应力理论和Kirchhoff板理论,建立了功能梯度微板热力耦合屈曲等几何有限元模型。该模型仅包含一个材料尺度参数,能够描述尺度效应现象,且满足修正偶应力理论的高阶连续性要求。基于虚功原理推导了功能梯度微板热力耦合屈曲等几何有限元方程。通过对板的典型算例分析,讨论了材料尺度参数、边长比及梯度指数对板稳定性的影响。结果表明,本文模型预测的屈曲载荷总是大于宏观理论的结果,即捕捉到了尺度效应现象;随着临界屈曲力的增加,临界屈曲热载荷线性减少;此外,边长比和梯度指数也对微板的稳定性产生一定影响。     

Temperature field analysis of IC molding process based on three dimensional finite element model

In the case presented in this paper, the distribution of temperature fields of the molding model during each time interval was obtained as the simulation proceeded along the molding time by using the 3D FEM with a simple division mesh. The simulation results indicate that the most temperature rise is located at the upper right hand corner of the die pad, while the least temperature rise during the molding process is located at the upper right hand corner of the lead frame. Based on the simulation results of the temperature field distribution in the molding model, we obtained the temperature variation trend as a result of changes in the geometric shapes of the molding model. Therefore, the information on the molding model and the analysis of temperature distribution during the integrated circuit molding process presented in this paper can be considered as references for the molding design for integrated circuit packaging process.     

几何精确NURBS有限元中边界条件施加方式对精度影响的三维计算分析

非均匀有理B样条(NURBS)有限元法把计算机辅助几何设计(CAGD)中的NURBS几何构形方法与有限元方法有机结合起来,有效消除了有限元离散模型的几何误差,提高了计算精度。但是由于NURBS基函数不是插值函数,直接在控制节点上施加位移边界条件会引起较大误差。本文详细讨论了NURBS基函数的插值特性,在NURBS有限元分析中采用罚函数法施加位移边界条件,提高了收敛率和计算精度。结合典型三维弹性力学问题,对两种施加位移边界条件的方法进行了对比和分析。计算结果表明,直接施加位移边界条件会导致收敛率和精度的明显降低,而基于罚函数法的NURBS有限元分析则能达到最优收敛率,并具有更高的精度。     

Variational principles of perforated thin plates and finite element method for buckling and post-buckling analysis

On the basis of the general theory of perforated thin plates under large deflections^{[1, 2]}, variational principles with deflectionw and stress functionF as variables are stated in detail. Based on these principles, finite element method is established for analysing the buckling and post-buckling of perforated thin plates. It is found that the property of element is very complicated, owing to the multiple connexity of the region. Project supported by National Natural Science Foundation of China.     

Mixed finite element and differential quadrature method for free and forced vibration and buckling analysis of rectangular plates

This paper presents a combined application of the finite element method (FEM) and the differential quadrature method (DQM) to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.     

Parallel finite element computation of incompressible magnetohydrodynamics based on three iterations

Based on local algorithms, some parallel finite element(FE) iterative methods for stationary incompressible magnetohydrodynamics(MHD) are presented. These approaches are on account of two-grid skill include two major phases: find the FE solution by solving the nonlinear system on a globally coarse mesh to seize the low frequency component of the solution, and then locally solve linearized residual subproblems by one of three iterations(Stokes-type, Newton, and Oseen-type) on subdomains with fine...     

Formulation of a semi-analytical approach based on Gurtin variational principle for dynamic response of general thin plates

4 semi-analytical approach for the dynamic response of general thin plates which employes finite element discretization in space domain and a series of representation in time domain is developed on the basis of Gurtin variational principles. The formulation of time series is also investigated so that the dynamic response of plates with arbitrary shape and boundary constraints can be achieved with adequate accuracy.Project supported by the National Natural Science Foundation of China     

基于小波有限元的车辆-轨道-桥梁系统竖向振动分析

基于小波有限元建立了车辆-轨道-桥梁系统竖向运动方程。将车辆、轨道和桥梁作为一个整体系统,钢轨和桥梁采用区间B样条小波单元离散,钢轨与桥梁之间的钢轨基础采用均布的弹簧和阻尼模拟,采用虚功原理建立了基于小波有限元的四轴车辆-轨道-桥梁竖向振动分析模型。结果表明,采用区间B样条小波单元可较大程度上减小系统的自由度数,缩减计算量,节省计算时间。     

基于有限材料参数试验数据的横观各向同性板结构随机有限元分析与验证

当材性试验数据有限时,为了研究各力学参数的离散性和不确定性对结构性能计算的影响,需要对材料参数采用随机变量建模并基于概率理论构建刚度矩阵的随机模型。为此,首先将随机弹性张量分解为一组基张量和由材料参数构成的随机系数的线性组合,以考虑刚度矩阵各分量间的统计相关性;并利用最大熵原理确定由上述随机系数组成的随机向量的概率密度函数。采用基于Metropolis-Hasting算法的马尔科夫链蒙特卡罗方法用于计算与之相关的概率模型的拉格朗日乘子,并通过Matlab生成材料参数的随机样本。最后采用蒙特卡罗随机有限元法对横观各向同性材料构成的板式结构在不同荷载下的力学行为进行了数值分析。以刨花板材料为典型案例,与试验结果对比,验证了本文方法的效果和实用性。     

STATISTIC MODELING OF THE CREEP BEHAVIOR OF METAL MATRIX COMPOSITES BASED ON FINITE ELEMENT ANALYSIS

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｃｒｅｅｐｂｅｈａｖｉｏｒｏｆｓｈｏｒｔｆｉｂｅｒｒｅｉｎｆｏｒｃｅＭｅｔａｌＭａｔｒｉｘＣｏｍｐｏｓｉｔｅｓ (ＭＭＣｓ)ｄｅｐｅｎｄｓｏｎｔｈｅｆｏｌｌｏｗｉｎｇｆａｃｔｏｒｓ,ｓｕｃｈａｓｔｈｅｃｒｅｅｐｐｒｏｐｅｒｔｙｏｆｔｈｅｍａｔｒｉｘ ,ｅｌａｓｔｉｃａｎｄｆｒａｃｔｕｒｅｓｐｒｏｐｅｒｔｉｅｓｏｆｔｈｅｆｉｂｅｒ,ｇｅｏｍｅｔｒｉｃｐａｒａｍｅｔｅｒｓｏｆｔｈｅｆｉｂｅｒｓ,ａｒｒａｎｇｅｍｅｎｔｏｆｔｈｅｆｉｂｅｒｓａｎｄｔｈｅｐｒｏｐｅｒｔｙｏｆｔｈｅｆ…     

基于显式有限元方法的两相介质弹塑性动力反应计算分析

针对增量形式的流体饱和两相多孔介质弹塑性波动方程组,运用基于显式逐步积分格式的时域显式有限元方法对该波动方程组进行求解,并应用基于SMP破坏准则的弹塑性动力本构模型描述两相介质的动力反应性质,对两相介质在输入地震波作用下的弹塑性动力反应进行计算和分析,将计算结果与相应的弹性动力反应的计算结果进行对比;对本文应用的弹塑性...