球面各向同性圆锥其顶端受力时的弹性力学解

本文在文［９］的基础上，研究球面各向同性圆锥顶端作用集中力，集中力矩时的位移和应力分布。最后讨论了空心锥顶端受力的问题。     

EXACT SOLUTIONS FOR FREE VIBRATIONS OF TRANSVERSELY ISOTROPIC CIRCULAR PLATES

By virtue of the general solution of dynamic elasticity equations for transverse isotropy as well as the variable separation method, three-dimensional exact solutions of circular plates are obtained under two types of boundary conditions. The solutions can consider both axisymmetric and non-axisymmetric cases. Solutions based on the classical plate theory and Mindlin plate theory are also presented under the corresponding boundary conditions. Numerical results are finally presented and comparisons between the three theories are made. The project is supported by the National Natural Science Foundation of China (No. 19872060).     

A theoretical solution of cylindrically isotropic cylindrical tube for axisymmetric plane strain dynamic thermoelastic problem

A dynamic thermoelastic solution of a cylindrically isotropic cylindrical tube or solid cylinder with axisymmetric plane deformations is developed. Since there exist thermal boundary conditions and tractions on the two surfaces of a cylindrical tube, the problem under consideration is with inhomogeneous boundary conditions. Therefore we introduce a special function to transform the inhomogeneous boundary conditions to homogeneous ones for an unknown function. Then by using the method of separation of variables, the unknown function can be expressed as the multiplication series of Bessel functions and unknown time functions. Thirdly, by virtue of the orthogonal properties of Bessel functions, the equations about these unknown time functions are derived and the solutions are obtained. Finally, the displacement is obtained by adding the two parts mentioned above. By means of the present method, integral transform can be avoided. It is suitable for arbitrary thermal loads and mechanical loads. Numerical results are also presented for thermal shocked, cylindrically isotropic cylindrical tube and solid cylinder. Project supported by the National Natural Science Foundation of China (No. 10172075 and No. 10002016).     

Several three-dimensional solutions for transversely isotropic functionally graded material plate welded with circular inclusion

The problem of a transversely isotropic functionally graded material (FGM) plate welded with a circular inclusion is considered. The analysis starts with the generalized England-Spencer plate theory for transversely isotropic FGM plates, which expresses a three-dimensional (3D) general solution in terms of four analytic functions. Several analytical solutions are then obtained for an infinite FGM plate welded with a circular inclusion and subjected to the loads at infinity. Three different cases are considered, i.e., a rigid circular inclusion fixed in the space, a rigid circular inclusion rotating about the x-, y-, and z-axes, and an elastic circular inclusion with different material constants from the plate itself. The static responses of the plate and/or the inclusion are investigated through numerical examples.     

Bending of functionally graded piezoelectric rectangular plates

By introducing two displacement functions as well as two stress functions, two independent state equations with variable coefficients are derived from the three-dimensional theory equations of piezoelasticity for transverse isotropy. A laminated approximation is used to transform the state equations to those with constant coefficients in each sub-layer. The bending problem of a functionally graded rectangular plate is then analyzed based on the state equations. Numerical results are presented and the effect of material gradient index is discussed. Supported by the National Natural Sciences Foundation of China (No. 10002016).     

界面特性对功能梯度智能梁静动态响应的影响研究

采用状态空间法分析了两边简支的含压电夹层的功能梯度梁的静力弯曲和自由振动问题．为了考虑中间压电层与上、下功能梯度层之间的粘结效果,采用线性弹簧模型以模拟界面性能．假设上下功能梯度层的材料参数沿厚度连续变化,而压电层则是均匀材料,并且它们都是正交各向异性的．由于功能梯度梁的不均匀性使得直接求解比较困难,文中用层合模型来进行近似．数值算例中,分别考虑了压电层用于传感器或作动器的情形,分析了粘结界面完美程度对组合梁静力弯曲和自由振动频率的影响．     

3维电介质击穿模型在雷电防护系统评估试验中的应用

 采用荷电圆盘雷云解析模型作激励源,利用电介质击穿模型进行了地闪先导放电高分辨力3维数值模拟,得到了50 m分辨力的地闪放电图样与先导近地500 m时的地面电场分布（峰值-164.9 kV·m_-1）,结果与实际观测值相符。模拟中通过高维样条插值实现了计算空间与评估区域的分辨力转换（50 m到1 m）,构建评估模型,可以进行雷电防护系统的数值评估试验。用该方案对一种雷电防护系统概念模型进行了试验,结果显示：系统10 m高、-1.5 MV激励的条件下,5 m高处的雷击概率以系统为中心随距离增加而增大,系统投影区域雷击概率为0;由于先导激励地面电场的非对称性,保护区范围各向分布极不均匀。通过此方案可以得到系统作用下精细的雷击概率分布,适用于雷电防护系统效能评估。