压电-压磁板条中反平面裂纹的电-磁-弹性分析

基于线性电磁弹性理论,获得了压电-压磁板条中反平面裂纹尖端附近的奇异应力、电场和磁场。假设裂纹位于和板条边界平行的中心位置,并且裂纹是电磁渗透型的。利用Fourier变换,将裂纹面的混合边值问题化为对偶积分方程,即而归结为第二类Fredholm积分方程。通过渐近分析,得到了裂纹尖端附近应力、应变、电位移、电场、磁场和磁感的封闭表达式。结果表明,对于电磁渗透裂纹,电场强度因子和磁场强度因子总为0;板条的宽度对应力强度因子有显著的影响;能量释放率总为正值。

ELECTRO-MAGNETO-ELASTIC ANALYSIS OF A PIEZOELECTROMAGNETIC STRIP WITH A FINITE CRACK UNDER LONGITUDINAL SHEAR

The singular stress,electric and magnetic fields in a piezoelectromagnetic strip containing a Griffith crack under longitudinal shear are obtained by the theory of linear piezoelectromagneticity.The crack is situated symmetrically and oriented in a direction parallel to the edges of the strip,which is assumed to be permeable.Fourier transforms are used to reduce the mixed boundary value problems of the crack to dual integral equations.The solution of the dual integral equations is then expressed in terms of Fredholm integral equations of the second kind.Closed forms of the stress,strain,electric displacement,electric field,magnetic field,and magnetic induction in the vicinity of the crack tip are derived by the use of asymptotic expansion.It is shown that,for the permeable crack,the electric field intensity factor(EFIF)and the magnetic field intensity factor(MFIF)are always zero;the width of the strip has significant influence on the stress intensity factors.The energy release rate is always positive.