周期分布压电纤维复合材料平面问题研究

为了探索压电纤维复合材料中局部应力场的分布规律和准确预测其有效刚度,基于复变函数理论和线性压电理论,得到了含周期分布压电纤维复合材料平面问题的半解析解。根据单胞内基体和夹杂所占区域的几何特点,分别给出复势函数的级数形式,这些复势函数在基体与夹杂的相邻界面上应满足连续性条件,在单胞的外边界应满足周期性边界条件和远场加载条件,从而确定复势函数中的待定系数,进而确定局部场,最后根据平均场理论给出了复合材料有效刚度和等效压电常数。结果表明:当基体模量大于压电夹杂模量时,电载荷对夹杂周围的局部应力场的影响是显著的,施加沿压电夹杂极化方向的正向电载荷有可能使基体与夹杂相邻界面上的最大等效应力位置相对于无电载或施加反向电载荷时发生90°改变;反之,电载荷对局部应力场几乎没有影响。由于微观结构的对称性,使得复合材料宏观上沿两个对称轴方向具有相同的刚度。同时还发现等效压电系数对基体模量非常敏感。     

Problem of Circular Hole in Thermopiezoelectric Media with Semi-permeable Thermal Boundary Condition

The semi-permeable boundary condition is proposed to discuss the influence of the thermal conductivity acting on the stress and heat flow around the hole. Based on the Stroh formalism, the closed form solutions are de- rived, the stress and heat flow around the hole are discussed. The results show that the thermal boundary condi- tion has significant influence on the hoop stress and heat flow around the hole. The hoop stress decreases dramatic- ally with the increasement of the thermal conduction coefficient.     

压电体表面Maxwell应力对断裂的效应

研究了压电固体外表面Maxwell应力和裂纹内表面Maxwell应力对断裂的效应。采用复变函数理论与Stroh公式,理论分析了半穿透裂纹内外环境介质对电场、裂纹张开位移以及裂纹应力强度因子的影响,并通过数值算例讨论了在纯电场作用下以及在力-电耦合载荷作用下裂纹的扩展行为。结果表明,压电体表面的Maxwell应力对裂纹的扩展有重要的影响。     

Coupled FEM Analyses on Electro-mechanical Problem of Electrostrictive Plate with Elliptical Hole

A detailed theoretical construction of general coupled 3D FEM analyses of anisotropic dielectrics is first presented by considering the electric body force and body couple moment. A 3D electrostrictive element is subsequently defined in ABAQUS user subroutine UEL and the post-processing of finite element method （FEM） results is realized by UVARM and dummy element method. Then the developed technique is used to solve the electro-elastic field of an isotropic electrostrictive plate with an elliptical hole subjected to electrical load. By comparing the coupled and uncoupled numerical results, the traditional uncoupled analytical method can cause a large error when the applied electric field or the electrostrictive performance of the dielectric is high, and thus the present coupled analysis is especially necessary.