Equivalent boundary integral equations for plane elasticity

Indirect and direct boundary integral equations equivalent to the original boundary value problem of differential equation of plane elasticity are established rigorously. The unnecessity or deficiency of some customary boundary integral equations is indicated by examples and numerical comparison.     

氮掺杂碳点的制备及其对阿莫西林高灵敏检测

以天然物质石斛为原料,一步水热法合成高荧光量子产率的氮掺杂碳点(NCDs),通过透射电子显微镜(TEM)、X射线光电子能谱(XPS)、傅里叶变换红外光谱(FT-IR)、紫外-可见光吸收图谱(UV-Vis)及荧光光谱(PL)对合成的NCDs进行表征。 实验结果显示合成的NCDs发强烈的蓝色荧光,呈现为球形或准球形,均匀分散,尺寸范围在1~5 nm;其表面含有丰富的COOH、OH和NH₂等水溶性基团,最佳激发和发射波长分别为350和435 nm,且具有良好的发光稳定性。 通过测定,合成的NCDs的荧光量子产率高达29.19%。在pH=7.4的缓冲溶液中测定不同物质对NCDs的荧光影响,相同条件下发现只有阿莫西林能够对NCDs荧光进行明显猝灭,表明合成的NCDs可选择性的识别阿莫西林,通过NCDs的荧光强度变化构建一种可灵敏检测阿莫西林的传感器,检测线性范围为2.6~30 μmol/L,检出限为0.15 μmol/L。     

ON THE FREE VIBRATION OF A SUBMERGED FGM HOLLOW SPHERE

The free vibration of a functionally graded material hollow sphere submerged in a compressible fluid medium is exactly analyzed. The sphere is assumed to be spherically isotropic with material constants being inhomogeneous along the radial direction. By employing a separation technique as well as the spherical harmonics expansion method, the governing equations are simplified to an uncoupled second-order ordinary differential equation, and a coupled system of two such equations. Solutions to these equations are given when the elastic constants and the mass density are power functions of the radial coordinate. Numerical examples are finally given to show the effect of the material gradient on the natural frequencies. The project is supported by the National Natural Sciences Foundation of China(No. 19872060).     

横观各向同性三维热弹性力学通解及其势理论法

通过引入两个位移函数，对用位移表达的运动平衡方程作了简化．利用算子理论，严格地导出了横观各向同性非耦合热弹性动力学问题的通解．对于静力学问题，通解的形式可进一步简化成用4个准调和函数来表示．具体考察了横观各向同性体内平面裂纹上下表面有对称分布温度作用的问题，推广了势理论方法，导出了一个积分方程和一个微分-积分方程．针对币状裂纹表面受均布温度作用情形，给出了具体的解。     

A general solution for static piezothermoelastic problems of crystal class 6mm solids

In this paper, a general solution for three-dimensional static piezothermoelastic problems of crystal class 6mm solids is presented. The general solution involves four piezoelastic potential functions and a piezothermoelastic potential function, of which four piezoelastic potential functions are governed by weighted harmonic differential equations. Compared with the general solution given by Ashida et al., in which seven potential functions are introduced, the general solution proposed in the present paper is more rigorously derived. Moreover, it has a simple form and is convenient for application. As an illustrative example, the problem of a pyroelectric half-space subjected to axisymmetric heating is studied. Numerical results of displacements stresses, electric potential and electric displacements are obtained for a cadmium selenide half-space. Thermally induced displacements and stress distribution are compared with those obtained for the same material without piezoelectric and pyroelectric effects. Project supported by the National Natural Science Foundation of China (19872060).     

三维裂纹体应力强度因子的计算

本文采用塌缩三棱柱形奇异单元的位移计算应力强度因子，给出了一个新的全三维外推公式，它是Ｃｈｅｎ和Ｋｕａｎｇ公式〔１３〕的全三维推广，特例证明，它的精度比Ｉｎ－ｇｒａｆｆｅａ和Ｍａｎｕ的公式〔８〕高一阶。数值计算表明，结果稳定和对单元尺寸改变不敏感     

各向同性和横观各向同性材料的统一点力解

本文根据横观各向同性弹性力学的通解获得了无限体的点力解，由它可以直接退化到各向同性情形的Ｋｅｌｖｉｎ解，利用这个点力解编制的边界元法程序，适用于横观各向同性材料也适用于各向同性材料，因此是真正的统一点力解。还用边界元法计算了两个数值例题。     

Elastodynamic solution of a non-homogeneous orthotropic hollow cylinder

A theoretical method for analyzing the axisymmetric plane strain elastodynamic problem of a non-homogeneous orthotropic hollow cylinder is developed. Firstly, a new dependent variable is introduced to rewrite the governing equation, the boundary conditions and the initial conditions. Secondly, a special function is introduced to transform the inhomogeneous boundary conditions to homogeneous ones. By virtue of the orthogonal expansion technique, the equation with respect to the time variable is derived, of which the solution can be obtained. The displacement solution is finally obtained, which can be degenerated in a rather straightforward way into the solution for a homogeneous orthotropic hollow cylinder and isotropic solid cylinder as well as that for a non-homogeneous isotropic hollow cylinder. Using the present method, integral transform can be avoided and it can be used for hollow cylinders with arbitrary thickness and subjected to arbitrary dynamic loads. Numerical results are presented for a non-homogeneous orthotropic hollow cylinder subjected to dynamic internal pressure. The project supported by the National Natural Science Foundation of China (10172075 and 10002016)     

正交各向异性压磁电弹性矩形板的稳定问题

从压磁电弹性力学的三维平衡方程和本构关系出发,推导得到了正交各向异性压磁电弹性矩形板稳定问题的状态方程。求解状态方程并结合边界条件得到了稳定问题的屈曲方程。给出了临界应力的算例。