压电、压磁材料球对称问题的通解

THE GENERAL SOLUTION OF SHPERE-SYMMETRIC PROBLEMS IN PIEZOELECTRIC/PIEZOMAGNETIC AND ELASTIC MEDIA

研究压电、压磁材料在球坐标系下 ,不计体力、体电荷和体电流的情况下 ,由平衡方程、梯度方程、压电和压磁的本构方程导出应力、应变、位移、电位移、电场强度、电位势、磁感强度和磁位势各未知量的通解 .考虑不同的边界条件 ,将其通解应用到应力、电学短路以及位移、电学开路和磁场分布的边界条件中 ,得到不同边界条件下问题的解 .

The fundamental equation of the sphere-symmetric problem in piezoelectric/piezomagnetic and elastic media under the spherical coordinate system is observed. The solution of the stress, strain, elastic displacement, electric displacement, intensity of electric field, intensity of magnetic field, electric potential and magnetism potential are derived by the balance equation, gradient equation and constitutive equation in which there are no body forces, free charges and body electric current. The general solution can be applied to difference boundary condition of stress, electric short-circuit and displacement, electricity open-circuit and magnetic field distribute.