磁电弹性圆锥顶端作用集中荷载的解析解

当磁电弹性材料特征根互异时，用5个势函数表示的通解出发，对圆锥顶端作用集中扭矩Mx的扭转、集中力Px和点电荷Q的压缩、集中力Px和集中力矩My的弯曲变形问题，用一些调和函数的线性组合分别构造了势函数，并根据边界条件求出了势函数中的待定系数从而确定势函数，再将势函数代入通解得到磁电弹性圆锥顶端作用集中载荷时的位移、电势、磁势、应力、电位移和磁感应强度的三维解析解。此解形式简单便于应用。当圆锥角2α=π时，可退化得到半空间问题的解。

Analytical Solutions of a Magnetoelectroelastic Cone under Concentrated Loads at Its Apex

When the characteristic roots of magnetoelectroelastic media are distinct, the general solutions of magnetoelectroelastic media were expressed with five potential functions. For the problem of a magnetoelectroelastic cone under concentrated loads (include torsional moment Mz leads to torsion, concentrated force Pz and point charge Q lead to compression, concentrated force Px and concentrated moment MN lead to bending) at its apex, the potential functions were constructed by a linear composition of a group of harmonic functions. The undetermined coefficients in the potential functions were determined by boundary conditions. Substituting the potential functions into the general solutions, the analytical three-dimensional solutions about the displacements, electric potential, magnetic potential, stresses, electric displacements and magnetic inductions were yielded for the magnetoelectroelastic cone subjected to concentrated loads. The solutions are simply in form and can be degenerated to the corresponding solutions of half-space problem when the apex angle 2a equals to .