General solutions of coupled thermoelastic problem

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横观各向同性热电材料简支矩形板的自由振动

从耦合的三维压电热弹性理论出发分析了横观各向同性热电材料简支矩板的自由振动,证明其存在两类振动,即解耦的第一类振动和耦合的第二类振动,如果板的结构和上下表面边界条件关于中面对称,则第二类振动又可进一步分解为对称振和反对称振动,给出了热电材料简支矩形板自由振动的三维精确解,采用Ｍｏｎｔｅ Ｃａｒｌｏ法克服了超越方程求复根的困难。对于ＰＺＴ－４矩形板给出了数值结果,分析了耦合效应对振动频率的影响,计算     

耦合热弹性问题的一般解

从线性化后的耦合热弹性基本方程出发,导出了一种新型式的一般解.在拟静态问题时,比Biot的解更简单,少一个势函数.     

EXACT SOLUTION TO THE PROBLEM OF A HALF-PLANE CRACK IN A TRANSVERSELY ISOTROPIC PIEZOELECTRIC BODY SUBJECTED TO ANTISYMMETRIC TANGENTIAL POINT FORCES

An exact and complete solution of the problem of a half-plane crack in an infinite transversely isotropic piezoelectric body is presented. The upper and lower crack faces are assumed to be loaded antisymmetrically by a couple of tangential point forces in opposite directions. The solution is derived through a limiting procedure from that of a penny-shaped crack. The expressions for the electroelastic field are given in terms of elementary functions. Finally, the numerical results of the second and third mode stress intensity factorsk ₂ andk ₃ of piezoelectric materials and elastic materials are compared in figures. Project supported by the National Natural Science Foundation of China (No. 19872060 and 69982009) and the Postdoctoral Foundation of China.     

正交各向异性金属板料的成形极限

１９９３年希尔提出了一个适用于各向异性材料的屈服准则,该文运用该屈服准则和马辛尼克－库祖斯基假设,建立了能够确定正交各是性金属料成形极限的控制方法半数值求解,分析了不同材料参数对成形极限图的影响。     

Natural frequencies of submerged piezoceramic hollow spheres

An exact 3D analysis of free vibration of a piezoceramic hollow sphere submerged in a compressible fluid is presented in this paper. A separation method is adopted to simplify the basic equations for spherically isotropic piezoelasticity. It is shown that there are two independent classes of vibration. The first one is independent of the fluid medium as well as the electric field, while the second is associated with both the fluid parameter and the piezoelectric effect. Exact frequency equations are derived and numerical results are obtained. The project supported by the National Natural Science Foundation of China (No. 19872060)     

压电材料圆锥顶端作用集中载荷的解

从压电材料三维问题的通解出发,用凑合法求解了圆锥顶端作用集中力、点电荷和集中力矩的解,此解形式简单便于应用。当圆锥顶角2α=π时,集中力、点电荷和扭矩的解可退化得到半空间问题的解。     

Numerical comparison of two boundary element methods for plane harmonic functions

A direct boundary element method (BEM) has been studied in the paper based on a set of sufficient and necessary boundary integral equations (BIE) for the plane harmonic functions. The new sufficient and necessary BEM leads to accurate results while the conventional insufficient BEM will lead to inaccurate results when the conventional BIE has multiple solutions. Theoretical and numerical analyses show that it is beneficial to use the sufficient and necessary BEM, to avoid hidden dangers due to non-unique solution of the conventional BIE.     

球面各向同性弹性力学的位移解法

本文引入三个位移函数（ｗ，Ｇ，ψ），将球面各向同性弹性力学运动方程，简化为关于ψ的二阶偏微分方程，和关于Ｗ和Ｇ的联立方程。在静力学问题中，联立方程可进一步简化，ｗ和Ｇ可用另一位移函数Ｆ表示，而Ｆ满足一个四阶偏微分方程。在球壳固有振动问题中，则简化为一个独立的二阶常微分方程，和另两个二阶的联立的常微分方程，证明了在多层球壳中，它们分别对应独立的两类振动。改进了常微分方程的解法，并计算了一个二层球壳的频率。     

Transient thermal stresses in an orthotropic hollow cylinder for axisymmetric problems

For the thermoelastic dynamic axisymmetric problem of a finite orthotropic hollow cylinder, one comes closer to reality to involve the effect of axial strain than to consider the plane strain case only. However, additional mathematical difficulties should be encountered and a different solution procedure should be developed. By the separation of variables, the thermoelastic axisymmetric dynamic problem of an orthotropic hollow cylinder taking account of the axial strain is transformed to a Volterra integral equation of the second kind for a function of time, which can be solved efficiently and quickly by the interpolation method. The solutions of displacements and stresses are obtained. It is noted that the present method is suitable for an orthotropic hollow cylinder with an arbitrary thickness subjected to arbitrary axisymmetric thermal loads. Numerical comparison is made to show the effect of the axial strain on the displacements and stresses. The project supported by the National Natural Science Foundation of China (10172075) and China Postdoctoral Science Foundation (20040350712)