摘要
A mode Ⅲ crack problem in a transversely isotropic piezoelectric material subjected to uniform loads at infinity is studied based on exact boundary conditions. The complex potential approach is used to reduce the problem to Hilbert problem. As a result, closed form field solutions in the piezoelectric material and inside the crack are presented. It is shown that the stresses and electric displacement have square root singularities at the crack tips, but the electric field is uniform everywhere in the material and equal to the remote applied one. It is also found that the electric displacement intensity factor depends on both material properties and the mechanical loads, but not the electric loads. Hence it may be concluded that the electric loads have no influence on the field singularities.
基于精确的边界条件，针对远处受均布外载作用的横观各向同性压电材料，研究了其内的Ⅲ型裂纹问题。应用复势的方法，该问题被化为Ｈｉｌｂｅｒｔ问题，从而分别给出了材料内及裂纹内封闭形式的场解。结果表明，电位移在裂纹尖端呈现平方根的奇异性，但电场在材料内是处处均匀的，且等于无限远处所施加的电载荷；结果还表明，电位移强度因子取决于材料常数和机械载荷，但与电载荷无关。因此可得结论：电载荷对场的奇异性无影响。
