正交异性复合材料J积分的研究

本文推导了正交异性复合材料板Ⅰ型裂纹Ｊ积分与位移导数的关系式，同时给出了应力强度因子Ｋ＿Ⅰ与位移的关系式，采用贴片云纹干涉法对三点弯曲粱进行了测试。由云纹图的位移场求出了Ｊ与Ｋ＿Ⅰ值，进而验证了正交异性复合材料板Ｊ与Ｋ＿Ⅰ的关系式的正确性。     

受外冲击的多刚体拉氏动力学方程

本文讨论了多刚体系统受外冲击的动力学响应问题,给出了其拉氏动力学方程,所得的方程便于计算机程式化计算。     

全息、散斑与云纹干涉的量程分析

本文以Fourier分析与光学统计为基础,以全息干涉的量程分析为主线,给出了全息干涉、散斑干涉与云纹干涉的最大可测位移表达式。首先由频谱分析给出了三种干涉间的相互关系,再由互相关分析得到了全息干涉法可测位移量与散斑平均尺寸间的关系式。散斑干涉与云纹干涉则作为全息干涉记录的两种特殊情况给出了其量程的上限。     

关于刚体系统的单侧约束运动

本文研究了一大类刚体系统的单侧约束运动的局部和整体性质。主要结论是;局部地,这类系统的运动相当于某带过黎曼流形上的质点的运动;整体地,在能量守恒的假定下。这类系统相当于某带边黎曼流形上的台球系统。     

推导刚体动力学方程的张量方法

本文提出了基于连续介质力学概念推导刚体动力学方程的张量方法,运用具有零共旋率的惯性张量的时间导数公式,证明了Lagrange方程、Nielsen方程、Gibbs-Appell方程、Kane方程和广义动量式Kane方程等五种方法的等价性,给出了角速度、角加速度之间的一些微分关系式.     

含摩擦的多刚体系统碰撞问题的滑动状态步进法

研究了含铰摩擦的多刚体系统的碰撞动力学问题．在保留了关于处理冲击问题的经典近似假定的基础上,给出了计算冲击后系统广义速度的滑动模式步进算法．该算法避免了求解变尺度的微分方程的困难,同时由于考虑了切向模式的复杂性,从而使计算结果避免了碰撞前后能量的不协调性．算例描述了该算法的实现过程．     

多刚体系统的外碰撞动力学方程

本文讨论了两个多刚体系统之间相互碰撞的动力学问题,给出了碰撞冲量和广义速度增量已经解耦的,且适合于计算机程式求解的外碰撞动力学模型,该模型具有实用价值。     

约束的NLS系统的刚体型Poisson结构

A constrained system associated with a 3×3 matrix spectral problem of the nonlinear Schrodinger(NLS) hierarchy is proposed. It is shown that the constrained system is a Hamiltonian system with the rigid body type Poisson structure on the Poisson manifold R3N. Further, the reduction of the constrained system extended to the common level set of the complex cones is proved to be the constrained AKNS system on C2N.     

矩阵位移法在连系梁计算中的应用

矩阵位移法是结构矩阵分析法的一种,矩阵位移法的基本体系和节点位移未知量的选择一般是唯一的,它容易编制通用的计算机程序,矩阵位移法又分为刚度法和直接刚度法,二者的基本原理并无本质区别,只在形成总刚度矩阵时使用方法不同,直接刚度法相对简便,应用也较广泛,本文研究直接刚度法在连续梁内力计算的应用.     

高维纵向数据群点的刚体结构检验方法

本文中, 我们提出一种检验高维纵向数据群点在运动中是否保持刚体结构的方法, 并给出高维群点变形系数的定义. 对群点刚体结构的检验, 可以把握群点运动的主要特征, 并便于对群点的未来运动趋势做总体预测. 通过仿真案例以及分析比较中国东部、西部城市群的经济发展过程中多元性的变化, 验证了方法的合理性和应用价值.     

锥壳的位移解及应用*

本文提出求锥壳方程通解的另一种方法——位移法.文中根据文献[1]给出的壳体基本关系,导出锥壳一般弯曲问题的位移方程组,然后通过引入一个位移函数U(s,θ)(在极限情况下,就变为对于圆柱壳所引入的位移函数),从而将锥壳基本方程组化成关于位移函数U(s,θ)的8阶可解偏微分方程(控制微分方程).对于一般弯曲问题,该方程的一般解以广义超几何函数给出;对于轴对称弯曲问题,用Bessel函数给出其一般解.作为锥壳位移解法的应用,讨论了Winkler地基模式上的锥壳的轴对称弯曲问题,给出数值结果.     

Application of amplitude–frequency formulation to nonlinear oscillation system of the motion of a rigid rod rocking back

The scope of this paper is evaluating an oscillation system with nonlinearities, using a periodic solution called amplitude–frequency formulation, such as the motion of a rigid rod rocking back. The approach proposes a choice to overcome the difficulty of computing the periodic behavior of the oscillation problems in engineering. We are to compare the solutions results of this method with the exact ones in order to validate the approach and assess the accuracy of the solutions. This method has a distinguished feature, which makes it simple to use and agree with the exact solutions for various parameters. Moreover, it is perceived that with one‐step iteration high accuracy of the solution will be achieved. We may apply the results of the solution to explain some of the practical physical problems. Copyright © 2009 John Wiley & Sons, Ltd.     

The convergence of iterative solutions to the Electric Field Integral Equation

The Jacobi iterative method is applied to the system of linear equations arising from the discretization of the Electric Field Integral Equation (EFIE). It is shown that the resulting matrix equation is a contraction mapping, guaranteeing monotonic mean square convergence, for any initial guess, and for a preferred choice of a relaxation parameter (). Both the criterion for convergence and for the generation of the initial guess are discussed in detail. Results are shown for the 2-dimensional TM scattering by a perfectly conducting strip which illustrates the major points of this paper. The mathematical criterion herein may be applied to any electromagnetic problem employing the EFIE for perfectly conducting surfaces.     

The Annihilating-Ideal Graph of a Commutative Ring with Respect to an Ideal

For a commutative ring R with identity, the annihilating-ideal graph of R, denoted 𝔸𝔾(R), is the graph whose vertices are the nonzero annihilating ideals of R with two distinct vertices joined by an edge when the product of the vertices is the zero ideal. We will generalize this notion for an ideal I of R by replacing nonzero ideals whose product is zero with ideals that are not contained in I and their product lies in I and call it the annihilating-ideal graph of R with respect to I, denoted 𝔸𝔾 _I (R). We discuss when 𝔸𝔾 _I (R) is bipartite. We also give some results on the subgraphs and the parameters of 𝔸𝔾 _I (R).     

The dual reciprocity boundary integral equation technique to solve a class of the linear and nonlinear fractional partial differential equations

In this paper, we apply the boundary integral equation technique and the dual reciprocity boundary elements method (DRBEM) for the numerical solution of linear and nonlinear time‐fractional partial differential equations (TFPDEs). The main aim of the present paper is to examine the applicability and efficiency of DRBEM for solving TFPDEs. We employ the time‐stepping scheme to approximate the time derivative, and the method of linear radial basis functions is also used in the DRBEM technique. This method is improved by using a predictor–corrector scheme to overcome the nonlinearity that appears in the nonlinear problems under consideration. To confirm the accuracy of the new approach, several examples are presented. The convergence of the DRBEM is studied numerically by comparing the exact solutions of the problems under investigation. Copyright © 2015 John Wiley & Sons, Ltd.