无限大压电准晶介质中两个圆柱夹杂的干涉作用

Interference of two cylindrical inclusions in an infinite piezoelectric quasicrystal medium

推导了含有两个圆柱状夹杂的无限大一维压电准晶介质在反平面作用力和平面内电载荷作用时的电弹性场。假设基体与夹杂之间的界面为完美粘结,利用保角变换技术和解析延拓理论,得到了圆柱状夹杂边值问题的解析解以及基体和夹杂内声子场和相位子场的应力以及电位移的解析表达式,结果显示电弹性场的分布与复合材料各相的材料参数、几何参数以及反平面作用力和平面内电载荷相关,数值算例表明了几何参数、材料性质和载荷大小对复合材料内部和界面上应力分布的影响,基于此研究了极限情形的圆柱状孔洞和刚性圆柱状夹杂问题。

The electro-elastic field of an infinite one-dimensional piezoelectric quasicrystal medium with two cylindrical inclusions is derived under the antiplane forces and inplane electric charge loads.Assuming a perfect bond at the interface between the matrix and the inclusions,the analytical solution of the cylindrical inclusions edge value problem and the analytical expressions for the stresses and potential shifts of the phonon and phase subfields in the matrix and inclusions are obtained using the angle-preserving transformation technique and the analytical extension theory.The results show that the distribution of the electro-elastic field is related to the material parameters and geometrical parameters of each phase of the composite as well as to the antiplane forces and in-plane electrical loads.Numerical calculations show the influence of geometrical parameters,material properties and load magnitude on the stress distribution within the composite and at the interface.Based on the general solution obtained,the limiting cases of cavity and rigidity inclusion problems were investigated.