变厚度夹层环形板的非线性弯曲

本文对具有变厚度的夹层环形板大挠度弯曲问题进行研究。利用变分原理导出表层和夹心均为变厚度的夹层环形板大挠度弯曲问题的控制方程和边界条件,进一步给出表层和夹心均为双曲型变厚度的夹层环形板大挠度方程,采用摄动法求得了具有双曲型变厚度夹层环形板在外边缘为可移夹紧固定、内边缘与一刚性中心固结情况下非线性弯曲问题的渐近解,得到内边缘处无量纲挠度与无量纲载荷和无量纲应力的解析表达式,并讨论几何参数和物理参数对夹层环板弯曲的影响。     

边界元法在薄板大挠度弯曲问题中的应用

本文提出一个用边界元法求解薄板大挠度弯曲问题的新途径。利用此方法计算了部分算例,其中圆板、椭圆板的计算结果与现有文献的结果进行了比较,证明了本方法是十分满意的。对于椭圆板,其结果比W.A.Nash得到的结果更接近试验值。本文还首次计算了正三角形及半圆形、半椭圆形板的大挠度弯曲问题,这些问题还尚未见到任何文献讨论过。     

反对称角铺设层合矩形板在不同边界条件下的后屈曲问题

本文以板的无量纲最大挠度为摄动参数,应用摄动法研究了在几种支承情况下,反对称角铺设层合矩形板的后屈曲问题,并以梁的特征函数所构成的广义付里叶级数作为高阶摄动偏微分方程的近似解,本文方法简捷,计算收敛性好、数据可靠。     

反对称角铺设层合矩形板在不同边界条件下的后屈曲问题

本文以板的无量纲最大挠度为摄动参数,应用摄动法研究了在几种支承情况下,反对称角铺设层合矩形板的后屈曲问题,并以梁的特征函数所构成的广义付里叶级数作为高阶摄动偏微分方程的近似解,本文方法简捷,计算收敛性好、数据可靠。     

单圆弧波纹管膜片的非线性大变形分析

采用拟壳法把单圆弧波纹管膜片看作具有初始挠度圆环薄板的组合结构,用非线性大挠度弯曲理论对单圆弧膜片的非线性大变形进行了分析。选取膜片圆弧部分的最大变形处挠度为摄动参数,采用板壳理论的修正迭代法,对外周边固定内周边自由的单圆弧波纹管膜片进行了求解,由边界条件和连续性条件得到了精确度较高的二次解析解。通过波纹管膜片圆弧的矢高和波长绘制了圆弧最大挠度处的特征曲线,随着单弧膜片的矢量高度的增加,膜片的挠度非线性增大,随着单弧波纹管膜片的弧长变长,膜片的挠度非线性增加。     

复合载荷下波纹管横向非线性弯曲摄动有限元法

采用新的小参数、将摄动法和有限元法相结合,研究了复合载荷作用下波纹管横向非线性弯曲的位移和应力分布。小参数为结构环向应变的均方根。将节点位移摄动展开,并以复合载荷的等效节点载荷为参考载荷,将其公共系数1摄动展开。由此划分载荷的级别、建立各级载荷和相应位移的关系,避免了常规的迭代运算。算例为一考虑自重的U型波纹管在注满水时的横向非线性弯曲问题。计算表明,波纹管的挠度和膜应力有非常显著的非线性效应;当最大挠度与壁厚之比达到5.1后本法将失效。本法在摄动小参数的选取和复合载荷的处理上有特色,能解决较大的挠度问题。     

挠度法和位移法对金属接骨板弯曲强度和弯曲刚度的影响

该文按照标准YY/T 0342—2020的要求,分别采用挠度法和位移法对3种不同规格型号的金属接骨板进行四点弯曲测试,计算出金属接骨板的弯曲强度和刚度。通过探讨2种测试方法的差异和数据分析,最终发现应用挠度法和位移法测定接骨板弯曲刚度的结果基本一致。但是,测定接骨板弯曲强度时,2种方法测得的结果差异较大,不能直接进行对比。这为金属接骨板的力学性能检验和研发过程中方法的选择提供了客观的数据及指导。     

双模量矩形板的大挠度弯曲计算分析

双模量矩形板在外载荷作用下,会形成各向同性的拉伸区和压缩区,把双模量矩形板看成两种各向同性材料组成的层合板,采用弹性力学理论建立了双模量矩形板在外载荷作用下的静力平衡方程,利用静力平衡方程确定了双模量矩形板的中性面位置,推导出了双模量矩形板的大挠度弯曲变形微分方程。用加权残值法求得了双模量矩形板的大挠度弯曲变形时板中点挠度,把该方法计算结果与有限元计算结果进行了比较,说明了该计算方法是可靠的,并讨论分析了双模量对矩形板大挠度弯曲变形的影响。     

板壳结构非线性随机有限元法研究

采用摄动随机有限元法研究了具有随机参数的板壳结构大挠度动力响应问题。基于Mindlin-Reissner板理论,采用全量Lagrangian法推导了具有板壳结构的大变形、大转动的动力响应有限元列式;通过基于等参变换的局部模型对随机场进行离散,结合摄动技术,建立了基于摄动技术的增量形式的随机有限元列式,计算结果与Monte-Carlo法相比较表明了该方法的有效性和精确性。通过该方法,为进一步进行结构可靠性分析提供了依据和方便。     

钢筋混凝土板弯曲问题的各向同性化域外奇点解法

本文提出了求解钢筋混凝土板弯曲问题的各向同性化域外奇点法。引入简单的坐标变换，将该问题转化成相应的各向同性板的弯曲问题，利用后者的简单格林函数，按域外奇点法求解。算例表明，这种方法简单，计算时间短，精度高。     

结构构件时程动力响应分析的半解析DQ法

本文提出了一种半解析DQ法，分析结构构件的时程动力响应。算例表明，半解析解DQ法的结果与解析解的结果非常一致。这种半解析的DQ法，通过引入类似文献[10]的推广的DQ单元，可以应用到较为复杂的结构的时程动力响应的求解。     

用微分求积法求解梁的弹塑性问题

根据梁塑性弯曲的工程理论,采用微分求积法进行了梁的弹塑性平面弯曲分析。微分求积法是一种直接求解微分方程(组)的数值方法,不依赖于变分原理,且能以较少的网格点求得微分方程的高精度数值解。与有限元分析结果的比较,表明了微分求积法求解梁的弹塑性问题的计算效率和精度。微分求积法的计算结果不受荷载步长的限制,也不需要迭代求解,特别对于承受非线性分布荷载作用的梁的弹塑性分析具有很大的优越性。通过选用不同的网格点数目,分析了微分求积法的稳定性和收敛性。     

Boundary reduction technique and triangular differential quadrature domain decomposition method for polygonal region

The differential quadrature method (DQM) is an attractive numerical method with high efficiency and accuracy. But the conventional DQM is limited in its application to regular regions by using functional values along a mesh line to approximate derivatives. To deal with problems on irregular geometric domains, coordinate transformation has to be conducted. The triangular differential quadrature method (TDQM) proposed by Zhong [Zhong H. Triangular differential quadrature. Commun Numer Meth Eng 2000; 16:401–8; Zhong H. Triangular differential quadrature and its application to elastostatic analysis of Reissner plates. Int J Solids Struct 2001; 38:2821–32], avoid the coordinate transformation. In this paper, the domain decomposition method (DDM) is used for the elliptical boundary problems on a pentagonal region. In every sub-domain, we solve the partial differential equations with TDQM. With boundary reduction technique, the functional values on internal points can be eliminated. The system of equations, which satisfied by the boundary points, can be obtained. Numerical results show that triangular differential quadrature domain decomposition method (TDQDDM) is easy and effective for treating the problems on irregular region.     

Application of generalized differential quadrature method to structural problems

This paper presents the first endeavour to exploit a generalized differential quadrature method as an accurate, efficient and simple numerical technique for structural analysis. Firstly, drawbacks existing in the method of differential quadrature (DQ) are evaluated and discussed. Then, an improved and simpler generalized differential quadrature method (GDQ) is introduced to overcome the existing drawback and to simplify the procedure for determining the weighting coefficients. Subsequently, the generalized differential quadrature is systematically employed to solve problems in structural analysis. Numerical examples have shown the superb accuracy, efficiency, convenience and the great potential of this method.     

Stability and accuracy of three Fourier expansion‐based strong form finite elements for the free vibration analysis of laminated composite plates

In the present paper, strong form finite elements are employed for the free vibration study of laminated arbitrarily shaped plates. In particular, the stability and accuracy of three different Fourier expansion‐based differential quadrature techniques are shown. These techniques are used to solve the partial differential system of equations inside each computational element. The three approaches are called harmonic differential quadrature, Fourier differential quadrature and improved Fourier expansion‐based differential quadrature methods. The improved Fourier expansion‐based differential quadrature method implements auxiliary functions in order to approximate functional derivatives up to the fourth order, with respect to the Fourier differential quadrature method that has a basis made of sines and cosines. All the present applications are related to literature comparisons and the presentation of new results for further investigation within the same topic. A study of such kind has never been proposed in the literature, and it could be useful as a reference for future investigation in this matter. Copyright © 2016 John Wiley & Sons, Ltd.     

Static and free vibration analyses of rectangular plates by the new version of the differential quadrature element method

A new version of the differential quadrature method is presented in this paper to overcome the difficulty existing in the ordinary differential quadrature method for applying multi‐boundary conditions in two‐dimensional problems. Since the weighting coefficients of the first derivative are the same as for the ordinary differential quadrature method even with the introduction of multi‐degree‐of‐freedom at the boundary points, the method is easier to extend to two‐ or three‐dimensional problems. A new version of the differential quadrature plate element has been established for demonstration. The essential difference from the existing old version of the differential quadrature plate element is the way the weighting coefficients are determined. The methodology is worked out in detail and some numerical examples are given to show the efficiency of the present method. Copyright © 2004 John Wiley & Sons, Ltd.     

Boundary integral equation supported differential quadrature method to solve problems over general irregular geometries

Based on the interpolation technique with the aid of boundary integral equations, a new differential quadrature method has been developed (boundary integral equation supported differential quadrature method, BIE-DQM) to solve boundary value problems over generally irregular geometries. The quadrature rule of the BIE-DQM is that the first and the second derivatives of a function with respect to independent variables are approximated by a weighted linear combination of the function values at all discrete nodal points and the corresponding normal derivatives at all boundary points. Several numerical examples are considered to verify the feasibility and effectiveness of the proposed algorithm.     

Numerical Solutions for Unsteady Flows of a Magnetohydrodynamic Jeffrey Fluid Between Parallel Plates Through a Porous Medium

In the present article, the numerical solutions for three fundamental unsteady flows (namely Couette, Poiseuille, and generalized Couette flows) of an incompressible magnetohydrodynamic Jeffrey fluid between two parallel plates through a porous medium are presented using differential quadrature method. The equations governing the flow of Jeffrey fluid are modeled in Cartesian coordinate system. The resulting non-dimensional differential equations are approximated by using a new scheme that is trigonometric B-spline differential quadrature method. The scheme is based on the differential quadrature method in which the weighting coefficients are obtained by using trigonometric B-splines as a set of basis functions. This scheme reduces the equation into the system of first-order ordinary differential equation which is solved by adopting strong stability-preserving time-stepping Runge–Kutta scheme. The effects of the sundry parameters of interest on the velocity profiles are studied and the results are presented through graphs. It is observed that, the velocity increases from the horizontal channel to vertical channel. The velocity is a decreasing function of magnetic parameter. With an increase in time, the velocity increases.     

On enforcement of corner conditions in triangular differential quadrature

This paper is concerned with the enforcement of corner conditions in the recently proposed triangular differential quadrature method. The sensitivity of solution to some corner conditions is exemplified and a reduced quadrature technique is introduced to overcome the sensitivity. Numerical examples in the context of bending and vibration of Mindlin plates are studied to validate the proposed reduced quadrature technique. It is shown that the technique is effective to cope with sensitivity of solution to corner conditions. The effect of the order of the reduced quadrature on accuracy of solution is also studied. It is found that satisfactory convergence is usually achieved when the order of reduced quadrature employed at a corner is larger than one half of the order of the triangular differential quadrature approximation in the entire triangle but two orders less than the order of the triangular differential quadrature approximation.     

Harmonic differential quadrature method and applications to analysis of structural components

Summary A harmonic differential quadrature (HDQ) method with application to the analysis of buckling and free vibration of beams and rectangular plates is presented. A new approach is proposed for the determination of the weighting coefficients for differential quadrature. It is found that the HDQ method is more efficient than the ordinary differential quadrature (DQ) method, especially for higher order frequencies and for buckling loads of rectangular plates under a wide range of aspect ratios. Also, some shortcomings existing in theDQ method are removed.