磁电弹性体中含不对称椭圆裂纹的动态与静态分析

Static and Dynamic Analysis for an Elliptic Hole with Asymmetry Edge Cracks in a Magnetoelctroelastic Body

通过拱形映射公式,利用复变函数方法研究了裂纹面上受反平面剪应力和面内磁电载荷共同作用下的磁电弹性体中含不对称椭圆运动裂纹与静态裂纹问题,导出了磁电全非渗透型边界条件下运动裂纹尖端场应力强度因子和机械应变能释放率的解析解.当运动速度为零时可退化为静止状态下的解.通过实例计算,分析了静止状态下受载荷的裂纹长度、椭圆的两轴长,以及磁、电和机械载荷对能量释放率的影响.

By conformal mapping formula and using the complex function method, problem of an elliptic hole with asymmetry moving edge cracks in a magnetoelectro- elastic body under the anti-plane shear stress and in-plane electric and magnetic loads was studied. The analytic solutions of the field intensity factors and the energy release rate were presented with the assumption that the surface of the crack was electrically and magnetically impermeable. When the velocity tends to zero, the analytic solutions can be degraded into a stationary state solution. In addition, under stationary state, some numerical examples were conducted to analyze the influences of loaded crack length, two axis length of elliptical, electric and magnetic loads on the energy release rate.