无限大压电材料薄板Ⅰ型裂纹断裂分析

Fracture Analysis of ModeⅠCrack in an Infinite Piezoelectric Plate

研究了含中心裂纹的无限大横观各向同性压电材料薄板的平面问题。利用压电材料平面应变问题的本构方程,通过引入两个适当的函数,将力学问题转化为偏微分方程组边值问题。利用复变函数方法和待定系数法,选取适当的应力函数,借助不可导通边界条件,确定未知系数,得到满足偏微分方程组边值问题的解。推导得到裂纹尖端附近的应力强度因子、应力场、电位移场和位移场、电势场的计算公式。

The plane problem around the center crack in an infinite transversely isotropic piezoelectric plate is studied.Mechanical problems can be converted to boundary value problems of partial differential equations by using the constitutive equations of piezoelectric material plane strain problem and introducing two proper functions.The unknown coefficients are determined with the aid of electrically-impermeable boundary conditions by using the complex function method and undetermined coefficients method and selecting the appropriate stress functions.The solutions of partial differential equations are obtained to fulfill boundary value problems.The computational formulas of stress intensity factor,stress,electric displacement and displacement and electric potential around the crack tip are further deduced.