Stochastic boundary element method in elasticity

The stochastic boundary element method is developed to analyze elasticity problems with random material and/or geometrical parameters and randomly perturbed boundaries. Based on the first-order Taylor series expansion, the boundary integration equations concerning the mean and deviation of the displacements are derived, respectively. It is found that the randomness of material parameters is equivalent to a random body force, so the mean and covariance matrices of unknown boundary displacements and tractions can be obtained. Furthermore, the mean and covariance of displacements and stresses at inner points can also be obtained. Numerical examples show that the proposed stochastic boundary element method gives satisfactory solutions, as compared with those obtained by theoretical analysis or other numerical methods. The project supported by the National Natural Science Foundation of China and the State Education Commission Foundation of China     

间隙元在钻柱瞬态动力学分析中的应用

为了描述钻柱与井壁的随机碰撞接触状态，本文构造了动力间隙元，并推导了动力间隙元的相对压缩量和迭代求解格式。把动力间隙元与梁单元相结合，采用Newmark直接积分法和冲量定理，进行了钻柱碰撞接触非线性瞬态动力学分析。经工程应用表明，构造的动力间隙元能够描述钻柱的碰撞接触状态，所设计的偏心防斜钻具已在大庆油田得到应用，取得了明显的经济和社会效益。     

POINT FORCE SOLUTION FOR A TRANSVERSELY ISOTROPIC ELASTIC LAYER

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轴对称界面端的扭转问题

基于弹性力学轴对称扭转问题的通解,研究了具有任意几何形状的双材料轴对称界面端,给出了界面端的应力奇异性及其附近的位移场和奇应力场,定义了扭转问题的Ｄｕｎｄｕｒｓ双材料参数。研究结果表明,应力奇异性只与界面端的结合角和扭转问题的Ｄｕｎｄｕｒｓ双材料参数有关,而与界面的角度以及界面端与对称轴之间的距离无关,在任何情况下,特征值均为实数,不会产生振荡应力奇异性。     

On the relationship between the lightning electromagnetic field and the channel-base current based on the TL model

A set of approximation expressions relating the lightning channel-base current and the lightning electric and magnetic fields on earth surface are proposed respectively in the near-zone and far-zone, by employing the transmission line (TL) model. The derived expressions show that, the electric and magnetic fields waveforms can be expressed approximately by the channel-base current waveform with different factors at a certain distances, whether in the near-zone or far-zone. The factors can be expressed in terms of the return stroke wavefront speed v, the speed of light c, and the horizontal distance r between the return-stroke channel and the observation point.     

正交各向异性功能梯度圆柱壳的自由振动

利用从弹性力学的三维基本方程导得的状态方程，结合层合近似模型，求得了柱型正交各向异性功能梯度圆柱壳的自由振动频率，给出了数值算例，并与前人结果作了比较，文末讨论了相关参数的影响。     

纤维端部的界面裂纹分析

基于弹性力学空间轴对称问题的通解,研究了短纤维增强复合材料中纤维端部的轴对称币形和柱形界面裂纹尖端的应力奇异性,得到了裂纹尖端附近的奇异应力场．研究结果表明,这两种轴对称界面裂纹尖端的应力奇异性相同,并且与平面应变状态下相应模型的应力奇异性一致,材料性能对裂纹尖端附近奇异应力场的影响可用三个组合参数描述     

Exact static analysis of a rotating piezoelectric spherical shell

This paper gives an exact analysis of a rotating piezoelectric spherical shell with arbitrary thickness. At first, three displacement functions are introduced to simplify the basic equations of a spherically isotropic, piezoelectric medium. By expanding the displacement functions as well as the electric potential in terms of spherical harmonics, the basic equations of equilibrium are converted to an uncoupled Euler type, second order ordinary differential equation and a coupled system of three second order ordinary differential equations. A general solution to the homogeneous equations of equilibrium is then derived. The static analysis of a rotating spherical shell is then performed and numerical example is presented. The project supported by the National Natural Science Foundation of China, the Zhejiang Provincial Natural Science Foundation, and the Japanese Committee of Culture, Education and Science.     

横观各向同性轴对称问题的加权残数法及其工程应用

利用文[1,5]的理论,本文提出用两个调和函数的方法求解横观各向同性的轴对称问题,将它引入加权残数法,推得了一系列简洁的边界型最小二乘配法公式,就结构工程和岩土工程的两个例题作了计算,得到了有用的结论。本文的方法比列赫尼茨基的重调和函数法更为简便。     

Determination of Formaldehyde with a Platinum–Palladium–Graphene Nanocomposite Glassy Carbon Electrode

The oxidation of formaldehyde on a platinum (Pt)–palladium (Pd)–graphene nanocomposite glassy carbon electrode prepared by chemical reduction was characterized in 0.5?M sulfuric acid. The surface and morphology of the catalyst were characterized by transmission electron microscopy, Raman spectroscopy, and X-ray diffraction. Bimetallic Pt–Pd nanoparticles were uniformly dispersed on the graphene sheets. Energy-dispersed X-ray spectroscopy was used to characterize the metal composition of the nanocomposite. The electrocatalytical characteristics of the modified electrode were investigated by cyclic voltammetry. The results show that the electrode displayed high activity for the oxidation of formaldehyde in sulfuric acid with a linear relationship from 4.50?µM to 0.180?mM and a detection limit of 2.85?µM. The low detection limit, wide linear dynamic range, and high sensitivity of the modified electrode suggests further applications.