一种四边形广义协调薄板弯曲单元

为了降低位移型任意四边形薄板弯曲有限元构造的难度,基于修正最小势能变分原理,提出了一种新的广义协调位移的设计方法,并且构造出一种任意四边形网格下的位移型薄板弯曲单元Q8P。这种单元能够通过常应力分片检查,当弯矩,扭矩和横向剪力沿着单元边界的分布为常值时,由于位移在单元边界非逐点协调而产生的附加能量为零。这种新型的广义协调单元保证了有限元解的收敛性,计算效率高,具有较高的数值精度,并且对网格畸变不敏感。     

基于三角形连接的有限元网格划分

文中创新地提出了三角形连接的有限元网格划分的算法,但是三角形并不是有限元计算的基本单元,而是根据已经生成的三角形生成较为规整的四边形。在实际的项目过程中,创新地提出了三种有效的算法,并利用C＋＋面向对象的MFC程序设计和编写。本程序可以从模型文件读取边界以及点约束和线约束特征数据,程序自动计算出一个较为合理的边界间距值,并且根据需要人工或自动选择一种划分算法,从而自动完成高质量的四边形网格划分。三种算法皆可以处理大量数据点和线,并且划分速度较为高效。本程序模块成功应用于有限元计算软件中。     

基于组合杂交变分原理的4节点轴对称元

本文基于组合杂交变分原理推导四节点的轴对称元,依据能量协调条件,导出含有8个参数的轴对称应力模式.其优越性能突出表现在离散模型对于计算背景(如单元畸变和材料的不可压缩性等)的广泛适应性.数值算倒结果表明,该轴对称元位移和应力明显优于其它的轴对称元.     

Windows环境下的有限元网格消隐算法

本文主要研究ＷｉｎＰｏｓｔ中有限元网格消隐问题。利用有限元法中使用的单元通常为凸休且其多形一般情况为三角形或四边形的特征，提出了十分有效的有限元网格边界面及可见前向边界面的布尔运算搜索算法，这大大减少了消隐算法的计算量，并且本文还提出了一种十分有效的 组合结构有限元网格的消隐法。     

栅格法三维六面体网格局部加密算法

有限元数值分析的精度和效率与网格单元的划分质量以及疏密程度密切相关,针对三维六面体网格单元之间疏密过渡必须平缓和协调的要求,提出了一套基于8分法的六面体网格加密模板,并给出了相应的数据结构和模板应用方式.为使所有加密单元都有相对应的加密模板,建立了加密信息场调整规则;对需要进行加密的区域首先补充加密单元,按照节点加密属性调整加密信息场,然后根据单元加密属性对加密单元进行分类,按照全加密单元、面加密单元、边加密单元以及过渡加密单元的顺序依次采用相应的模板进行加密,从而实现三维六面体网格的局部协调加密.实例结果表明,采用该套加密模板的六面体网格局部加密算法能够保障密集网格向稀疏网格的平缓和协调过渡,所生成的网格可满足有限元数值计算的要求.     

平面应力问题新型广义有限元法

结合广义有限元和理性有限元的优势,针对平面应力问题提出一种新型广义四边形单元.该单元考虑泊松效应,以节点位移自由度约束弹性力学平面应力方程的半解析解,构造单元位移模式的附加项,较准确地反映真实位移场,提高单元的计算精度.推导新型广义单元及其等参单元的形函数公式,设计分片试验和数值算例验证单元的精度.数值算例结果表明：在规则网格和非规则网格下新单元的计算精度均优于传统有限元和广义有限元.新单元具有精度高且易于程序实现的特点,可推广应用到实际工程的结构分析中.     

有限元计算结果的可视化处理

有限元计算结果的可视化是分析有限元计算结果的重要手段. 提出了一种适用于任意形状单元的彩色云图的通用生成方法,并给出了四节点四边形单元彩色云图的生成算例.该算法简洁,高效,易于推广.     

一种基于多边形剖分的有限元网格生成方法

在两步网格化过程中,待分析区域首先被剖分为具有三条或四条边的简单子区域部分.然后将利用传递模板法或映射法对这些子区域进行网格生成.本文结合计算几何和有限元网格自动生成问题,给出了一种基于简单多边形剖分的全四边形有限元网格自动生成方法.该方法分两步实现有限元网格生成首先通过权函数的引导,对待分析的简单多边形区域先进行子域剖分,得到一组三角形和凸四边形子域(大单元)的集合;然后利用中点剖分方法,将三角形和凸四边形子域单元剖分为全四边形有限元网格.实践证明,本文提出的方法实现简单、使用灵活,结果网格的质量良好.     

基于四边形面积坐标法的广义协调薄板单元

为克服等参坐标的缺点,采用四边形面积法构造一系列4节点12自由度的广义协调任意面积坐标四边形薄板(Area-coordinate Quadrilateral Plate,AQP)单元.对广义协调条件、边界位移场和试函数的选取规律进行深入探讨.该系列单元克服等参单元易网格畸变的缺点,在推导过程中引入广义位移的特征矩阵、节点位移的特征矩阵以及转换矩阵的概念,以使推导过程简单化、通用化.数值算例表明,此方法通用性强、易于程序化,所构造的单元自由度少、效率和精度较高.     

基于能量统一格式的多尺度有限元法

为分析简单晶体多尺度有限元计算的能量构成,利用能量最小原理得到在统一理论框架下多尺度有限元计算的统一格式,表明有限元计算可以在微观原子尺度下和在宏观连续介质尺度下进行多尺度有限元计算.基于简单晶体变形的特点说明过渡单元设计应遵守的原则,并指出理想过渡单元应该是类似于晶体结构的单元,对于较复杂的晶体,则应该利用空间群方法充分研究具有230种空间群的过渡单元的性质.引用EIDEL等的纳米压痕计算结果作为算例,表明在计算中无虚拟插值点,多级晶胞单元具有与原单胞相同的点群操作且位移场插值受晶体中原子间键长的约束.     

A hybrid/mixed model finite element analysis for buckling of moderately thick plates

Two modified complementary energy principles which only require C⁰ fields are derived in this paper. It is pointed out that if the fields of moment and deflection satisfy the respective second order homogeneous differential equation then they can both be considered as independent of each other and satisfy the equilibrium equation. The linear fields of moment and deflection are used in finite element analysis. The calculated results show that the method used in this paper is simple and reliable.     

某型整体式抗侧滚扭杆的弯曲变形分析

针对某型整体式抗侧滚扭杆在弯矩作用下产生的弯曲变形现象,通过理论公式计算结合有限元分析软件对其弯曲挠度进行研究,并将其与实测变形量进行对比分析,所得弯曲变形结果可供工程师在结构设计时作为空间干涉校核参考.     

均布荷载下四边固支矩形薄板的挠度研究

为求解四边固支矩形薄板在均布荷载作用下的挠度表达式,本文利用叠加法以利维解为基础将复杂问题分解为多个简单问题,然后进行叠加,获得了四边固支矩形薄板在均布荷载作用下的挠度表达式。利用有限元模拟验证表达式的正确性,研究发现有限元结果与公式结果吻合较好,本文利用叠加法求得的挠度表达式具有较高的求解精度,且表达式具有良好的收敛性。基于现有资源,推导出均布荷载下固支矩形薄板的挠度表达式,可供相关人员参考。     

A hybrid finite element method for stokes flow: Part II—Stability and convergence studies

In Part I we have presented a hybrid finite element method based on an assumed stress field which has the features: (i) the unknowns in the final system of finite element equations are (a) the nodal velocities, and (b) the ‘constant term’ in the arbitrary pressure field over each element; (ii) ‘exact’ integrations were performed for each element.In the following we present studies of stability and convergence of the above hybrid finite element method.     

小波神经网络在基坑变形预测的研究与应用

针对一般小波神经网络存在的学习时间长,网络预测精度低的问题,提出了对网络输入层权值初始值进行归一化处理的优化方法,改进了原有小波神经网络。将改进后的模型应用于某市轨道交通1号线珠江路站深基坑水平变形预测中。监测结果表明,网络输出值与实测值吻合很好,优化后的小波神经网络收敛速度也更快;同时随着大量最新的监测数据输入到网络中学习,将使深基坑水平变形预测更加精确。     

Large deflection analysis of plates and shells by discrete energy method

The discrete energy method—a special form of finite difference energy approach—is presented as a suitable alternative to the finite element method for the large deflection elastic analysis of plates and shallow shells of constant thickness. Strain displacement relations are derived for the calculation of various linear and nonlinear element stiffness matrices for two types of elements into which the structure is discretized for considering separately energy due to extension and bending and energy due to shear and twisting. Large deflection analyses of plates with various edge and loading conditions and of a shallow cylindrical shell are carried out using the proposed method and the results compared with finite element solutions. The computational efforts required are also indicated.     

Optimal design of hybrid laminated composite plates with dynamic and static constraints

Optimization procedures are presented that consider the static and dynamic characteristic constraints for laminated composite plates and hybrid laminated composite plates subject to a concentrated load on the center of the plate. The design variables adopted are ply angle or ply thickness. Considered constraints are deflection, natural frequency and specific damping capacity. Using a recursive linear programming method, nonlinear optimization problems are solved, and by introducing the design scaling factor, the number of iterations is reduced significantly. Relating interactive optimization procedures with the finite element method analysis, various hybrid composite plates with arbitrary boundary conditions can be designed optimally. In the optimization procedure, verification of analysis and design of the laminated composite plates are compared with a previous paper. Various design results are presented on laminated composite plates and hybrid laminated composite plates.     

Deflection analysis of expanded open-web steel beams

The finite element method is very appropriate for calculating stresses at isolated areas of expanded open-web steel beams. For deflection analysis, however, the entire beam, or one-half the beam if the system is symmetrical, must be included in the idealization and therefore it is not practical to obtain deflections by a direct application of the finite element method. In this paper, the authors present a method of deflection analysis which treats the castellated beam as an assemblage of typical segments and utilizes the finite element method to form the stiffness matrix for the typical segment. The beam deflections at the panel points are then computed by the conventional stiffness method. Two different idealizations were tried for the finite element analysis of a typical segment. These idealizations resulted in a 13 × 13 and a 7 × 7 stiffness matrix. Deflection values calculated by using the 7 × 7 stiffness matrix showed close agreement with those obtained experimentally.     

Macro-element analysis of skewed and triangular orthotropic thin plates with beam boundaries

A generalized macro-flexibility analysis of stiffened orthotropic skewed and triangular thin plates with beam stiffened boundaries subjected to bending and stretching is presented. The proposed method accounts for minimized number of elements in a domain, i.e. the element size is independent of the final results. This is accomplished by satisfying the equilibrium and compatibility conditions along the nodal lines interconnecting contiguous elements. The solution form and shape functions of element shapes are a combination of Fourier series and polynomials with undetermined coefficients. To obtain a solution of a general domain, the orthotropic triangular and parallelogram macro-plate elements with edge beams, satisfying moment and shear equilibrium conditions along nodal lines, were assembled and analyzed by utilizing compatibility of deflection and slope. The results from the proposed methodology were compared to the ones from the finite element method. Also, the convergence was checked by increasing the number of harmonics. The study indicates that good convergence is observed within the first four harmonics.     

Macro-element analysis

In recent years methods of analyzing plates in bending via large or macro-element have been studied. Herein, a method of studying plate behavior by a macro-flexibility approach is introduced. Deflected shapes of macro-elements of rectangular shapes were obtained by a shape function that satisfies all four boundary conditions and the bi-harmonic equation. The shape functions were a sum of sinusoidal and polynomial terms with undetermined coefficients. The elements that satisfy moment and shear conditions, were assembled by utilizing compatibility equations for deflection and slope. This resulted in equilibrium of forces and moments for all lines along the common edges of macro-elements. Three bounded domains were analyzed, and the results were compared to solutions obtained from classical and finite element methods. The convergence of the macro-approach was checked by progressively increasing the number of harmonics. The study of the numerical results indicates that excellent results can be obtained within the first three harmonics.