动态环板元的动刚度矩阵

本文对于环形薄板单元取包含贝塞尔函数的谐振变形作为形状函数,解决了关于特殊函数的复杂积分问题.从而精确推导了环形单元的动刚度矩阵,并用直接刚度法进行了校核.接着,又着重于将封闭形式的动刚度矩阵,按频率平方的升幂式展开,得到了简洁完备的结果,以此作为结构动力特性分析和响应计算的基础.     

分析复合材料层合板弯曲和振动的一种有效无网格方法

基于高阶剪切法向变形板理论（HOSNDPT）利用无网格方法对层合板弯曲和振动问题进行数值分析.在通常的径向点插值法（RPIM）中对每个Gauss(高斯)点或计算点需要求矩矩阵的逆,且受到影响域半径大小的限制.而在加权节点径向点插值法（WN-RPIM） 近似中,求解系统矩阵的逆的数量等于问题域中的节点数量,它远远小于Gauss点的数目,可以大大减少矩矩阵求逆的计算量,且克服了RPIM中影响域半径大小的限制.首先,将三维板位移分解成厚度和面内位移的乘积,在厚度方向使用正交Legendre多项式作为基函数,在板的面内使用WN RPIM来构造形函数.然后,通过对层合板的弯曲问题进行数值计算表明WN-RPIM的计算精度和稳定性.最后,将该方法推广到对不同边界条件、不同厚跨比、不同铺设方式的层合板振动问题的数值计算,数值结果表明了本文提供方法的适用性和有效性.     

缓变厚度中厚板的自由振动

本文将中厚板的厚度函数按一小参数展开,并采用奇异摄动方法,把原来变系数的微分方程组化成一系列常系数微分方程组求解.文中给出了任意变厚度中厚板的自振频率计算显式表达式,由此式,我们不仅可以方便地计算出各种变厚度的自振频率值,而且也可以根据频率的要求来优化板的厚度.文中的算例表明,本文的方法具有较好的精度、方法简便、有效等其他优点,可以考虑作为分析各种变厚度板壳的振动及稳定特征问题的有效方法之一.     

具有几何对称性的12参数矩形板元

1 引言 三角形板元中,形式最简单的是九参数元,节点参数是单元三个顶点上的函数值和两个一阶偏导数值,非协调九参三角形板元的研究取得了丰硕成果,根据不同方法已构造出多种收敛性能好的单元.相比之下,矩形板元的研究较少见报道.矩形板元中形式最简单的是12参元,节点参数是单元4个顶点上的函数值和两个一阶偏导数值,这类似于九参三角形板元.常见的12参矩形板元是ACM元,其形函数空间是完整3次多项式空间加上两个4次多项式的基函数,ACM元是C°元,但位移形函数的外法向导数平均值在单元间不连续,这类似于Zienkiewicz九参三角形板元,但由于矩形单元的特殊形状,ACM元是收敛的.龙驭球教授等在[1]中提出一种12参矩形广义协调元,其位移形函数的外法向导数平均值在     

梯形板弯曲问题的康托洛维奇解

在康托洛维奇对矩形板弯曲问题的有效近似解的基础上,本文进一步探讨了在不同边界条件下的梯形板弯曲问题的康氏解法.将板的位移用一级近似位移函数ω(x,y)=u(x,y)v(y)表示,式中, 在x方向的位移采用广义梁函数,用最小势能原理建立起对应于不同边界条件下的关于y方向位移函数v(y)的变系数常微分方程,求解微分方程,并利用边界条件,求出v(y)的精确解,从而可得到近似程度较高的梯形板弯曲问题的解.     

复合材料平面断裂中的J积分

本文采用复变函数方法,首先将裂纹尖端应力和位移代入J积分的一般公式得到了线弹性正交异性复合材料单向板复合型裂纹尖端的J积分的复形式,其次证明了该J积分的路径无关性,最后推出了该J积分的计算公式.作为特例,给出了线弹性正交异性复合材料单向板Ⅰ,Ⅱ型裂纹尖端的J积分的复形式,路径无关性和计算公式.     

含孔洞有限板与加固板的连接问题的分区广义变分原理解法

本文提出了一种新的有限元解法,采用复变函数作为有限单元模式,结合运用分区广义变分原理,解决了经贴焊加固板后的含孔洞有限板应力集中系数的计算问题,得到了级数形式的解析解.计算实践表明,本方法成功地分析了加固板与含孔洞有限板在焊接线上的位移连续和内力平衡问题.由于仅需划分三个单元,故与常规有限元方法比较,本方法可大大节约计算机内存,提高精度,降低计算时间.应力集中系数和焊接线处应力的数值计算结果列于诸表之中,可供工程技术人员设计参考.     

任意厚度具有自由边叠层板的精确解析解

自由边问题一直是三维弹性力学中的难题,通常很难满足自由边上一个正应力和两个剪应力都等于0．基于三维弹性力学基本方程和状态空间方法,引入自由边界位移函数并考虑全部弹性常数,建立了正交异性具有自由边单层和叠层板的状态方程．对状态方程中的变量以级数形式展开,通过边界条件的满足精确求解任意厚度具有自由边叠层板的位移和应力,此解满足层间应力和位移的连续条件．算例计算表明,采用引入的位移函数形式,简化了计算过程并且采用较少的级数项可以获得收敛解．与有限元方法计算结果进行了对比,可以得到较高精度的数值结果．其解可以作为其它数值方法和半解析方法的参考解．     

Steklov特征值问题的一种有效的Legendre-Galerkin谱逼近

本文给出Steklov特征值问题基于Legendre-Galerkin逼近的一种有效的谱方法.首先利用Legendre多项式构造了一组适当的基函数使得离散变分形式中的矩阵是稀疏的,然后推导了2维及3维情形下离散变分形式基于张量积的矩阵形式,由此可以快速地计算出离散的特征值和特征向量.文章还给出了误差分析和数值试验,数值结果表明本文提出的方法是稳定和有效的.     

流固冲击下加筋板的非线性动态屈曲

分析了流固冲击下加筋板的非线性弹性动态屈曲．考虑板与筋的膜力,忽略面内位移,运用Hamilton变分原理,得出非线性控制方程,采用双级数形式的挠度假设,由Galerkin方法得到离散方程组,根据Budiansky-Roth(B-R)曲线,判断加筋板的动态屈曲．     

Stability analysis of frame structures by bubble-function method

In the stability analysis of frame structures, the results by conventional finite element method (FEM) in which one member is taken as one element are sometimes unavailable. This paper took a new basic function system with bubble functions as the shape function of a bar element to develop a bubble function finite element method (BFEM), in which the bending and the geometric stiffness matrices were derived from the principle of virtual work. Bubble functions are finite element modes that are located entirely within a single element and are zero on boundaries of the element, but are nonzero at the other points. BFEM is as concise as conventional bar FEM but has better accuracy, and is adaptable to the buckling analysis of all kinds of frame structures. The use of bubble functions significantly improves the convergence of finite element analysis, and efficiently reduces the computation cost for the buckling analysis of frame structures. Numerical results show that using bubble functions in finite element for the stability analysis of structures is very efficient, especially for high-rise and large-scale frame structures.     

p－version有限元的快速高精度算法

ｐ－ｖｅｒｓｉｏｎ有限元的快速高精度算法曹礼群（湘潭大学）ＴＨＥＦＡＳＴｐ－ＶＥＲＳＩＯＮＦＩＮＩＴＥＥＬＥＭＥＮＴＭＥＴＨＯＤＷＩＴＨＨＩＧＨＡＣＣＵＲＡＣＹ￥ＣａｏＬｉ－ｑｕｎ（ＸｉａｎｇｔａｎＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓ...     

频域有限元计算的扩展面向目标误差估计

研究了针对频域有限元直接动态分析的面向目标误差估计以及误差范围估计计算方法．面向目标的误差估计方法就是专门针对如何准确和经济地估算特定值误差的一种方法,利用原问题的共轭偶问题进行计算．频域有限元的直接动态分析是模拟频域扫描实验的一种计算方法,专门针对谐振激励的线性动态响应问题,利用将原自由度分解为实部和虚部描述频率的变化,从而计算变形体的动态响应．利用扩展针对有限元的面向目标误差估计的自由度,将该方法应用到直接动态分析中进行误差估计．通过建立同时包含实部和虚部自由度的能量弱形式及偶问题,并将其数值实现,估算频域直接动态分析有限元解的误差及误差范围,并通过悬臂梁的激振算例进行了验证．     

Free vibration analysis of spatial Bernoulli–Euler and Rayleigh curved beams using isogeometric approach

This paper deals with the linear free vibration analysis of Bernoulli–Euler and Rayleigh curved beams using isogeometric approach. The geometry of the beam as well as the displacement field are defined using the NURBS basis functions which present the basic concept of the isogeometric analysis. A novel approach based on the fundamental relations of the differential geometry and Cauchy continuum beam model is presented and applied to derive the stiffness and consistent mass matrices of the corresponding spatial curved beam element. In the Bernoulli–Euler beam element only translational and torsional inertia are taken into account, while the Rayleigh beam element takes all inertial terms into consideration. Due to their formulation, isogeometric beam elements can be used for the dynamic analysis of spatial curved beams. Several illustrative examples have been chosen in order to check the convergence and accuracy of the proposed method. The results have been compared with the available data from the literature as well as with the finite element solutions.     

A dynamic multiscale lifting computation method using Daubechies wavelet

An important property of wavelet multiresolution analysis is the capability to represent functions in a dynamic multiscale manner, so the solution in the wavelet domain enables a hierarchical approximation to the exact solution. The typical problem that arises when using Daubechies wavelets in numerical analysis, especially in finite element analysis, is how to calculate the connection coefficients, an integral of products of wavelet scaling functions or derivative operators associated with these. The method to calculate multiscale connection coefficients for stiffness matrices and load vectors is presented for the first time. And the algorithm of multiscale lifting computation is developed. The numerical examples are given to verify the effectiveness of such a method.     

Model updating for undamped gyroscopic systems with connectivity constraints

ABSTRACT

An important and difficult aspect for the finite element model updating problem is to make the updated model have physical meaning, that is, the connectivity of the original model should be preserved in the updated model. In many practical applications, the system matrices generated by discretization of a distributed parameter system with the finite element techniques are often very large and sparse and are of some special structures, such as symmetric and band structure (diagonal, tridiagonal, pentadiagonal, seven-diagonal, etc.). In this paper, the model updating problem for undamped gyroscopic systems with connectivity constraints is considered. The method proposed not only preserves the connectivity of the original model, but also can update the analytical matrices with different bandwidths, which can meet the needs of different structural dynamic model updating problems. Numerical results illustrate the efficiency of the proposed method.     

An efficient backcalculation algorithm of time domain for large-scale pavement structures using Ritz vectors

This paper describes a backcalculation algorithm to determine the layer moduli and damping coefficients in the time domain for large-scale pavement structures. Pavement is modeled by three-dimensional finite element (3D FE). The parameter identification procedure makes use of Ritz vectors to reduce the size of matrices involved in the forward dynamic response analysis and the deflection sensitivity analysis. An exact complex mode superposition technique is used to obtain the dynamic response of the reduced equation system in the time domain. This method is more efficient, accurate and stable. The parameter estimates are improved iteratively by means of an algorithm that calls the finite element program of dynamic response analysis as a subroutine combining truncated singular value decomposition (TSVD) method. Simulation of a numerical solution validates the efficiency of the proposed method. Finally, the method is implemented for two experimentally tested sections of semiflexible pavement. All parameters are determined using the surface deflections of pavement experimentally recorded at the sensor locations of falling weight deflectometer (FWD).     

线弹性结构非平稳随机振动分析的有限元方法

当前结构分析的有效方法是有限单元法,对于结构动力学问题,将变位、应力等物理量通过Fou-rier变换进行谱分解,在谱分解的形式下推求动力刚度矩阵,这样所得的矩阵和有关方程不能用结构的随机振动问题常用的振型分解法求解.本文提出了一个普遍化的求解方法.文中考虑如地震、风震等外载是如下非平稳随机过程:P(t)={P_i(t)},P_i(t)=α_i(t)P_i0(t),α_i(t)是巳知的时间函数,P_i0(t)是平稳随机过程.本文将有限单元法所得的离散化方程进行Fourier变换,利用随机过程谱分解的正交增量性质推导了激励谱和反应谱之间关系的公式.用这些公式可以寻求反应的互功率谱密度矩阵,再根据反应的统计量进行结构的安全度分析.在本文提出的计算方法中,当α_i(t)=1(i=1.,2,…,n)时方法可以简化为求解平稳过程的特殊情况.在实际应用中可以根据地震、风震记录所得的功率谱密度矩阵,按本文方法用计算机对高层、高耸、大跨度等结构问题进行分析,为了说明计算方法的特点,文中首先考虑单自由度情况,其次考虑多自由度情况,列出几个重要统计量的计算公式,并对数值计算方法和安全度分析作了讨论.     

Convenient system of FEM test functions for computational fluid dynamics

For the development of finite element schemes, a fundamentally new system of test functions defined on a finite element that is a convex quadrilateral is proposed. Due to the remarkable properties of the system (specifically, mutual orthogonality), the resulting matrices can be simplified and the corresponding construction procedures can be made more transparent, especially for problems in computational fluid dynamics. Thus, the system of test functions may play an important role in finite element methods as applied to two-dimensional problems.