【摘要】 利用Stroh公式求得二维无限大电磁介质中椭圆孔口在无穷远均匀的力—电—磁载荷作用下的解析解。当椭圆的短半轴趋近零时 ,椭圆孔口变为裂纹 ,从而得到裂纹问题在精确边界条件下的解析解。所得结果表明 ,应力强度因子只与机械载荷有关 ,而电位移强度因子和磁感应强度因子不仅与外加的力—电—磁载荷有关 ,而且也与参数之比α β和α γ有关 ,其中α为椭圆孔口的短半轴与长半轴之比 ,β为孔口内介质的介电系数与电磁介质的当量介电系数之比 ,γ为孔口内介质的磁通率与电磁介质的当量磁通率之比。最后讨论了裂纹对电场和磁场的可导通性更多还原

【Abstract】 The elliptic cavity problem in an infinite magnetoelectroelasic plane under the remotely uniformly applied combined mechanical-electric-magnetic loadings is studied by using the Stroh formalism. The solution for a crack is obtained when the minor axis of the elliptic cavity approaches zero. The results demonstrate that the stress intensity factors depend only on the applied mechanical loading, but the electric displacement intensity factor and the magnetic induction intensity factor depend on the applied mechanical-electric-magnetic loadings as well as the two ratios of α/β and α/γ, where α is the ratio of the minor axis to the major axis of the ellipsoidal cavity, β is the ratio of the dielectric constant of the material in the cavity to the effective dielectric permittivity of the magnetoelectroelasic medium, and γ is the ratio of the magnetic permeability of the material in the cavity to the effective magnetic permeability of the magnetoelectroelasic medium. Electrically (or magnetically) permeable and impermeable cracks are two limiting or extreme cases of α/β (or α/γ)→0 and α/β(or α/γ)→∞, respectively. The intensity factors for several limiting cases are calculated.更多还原