By solving the piezothermoelastic control

equations and using the recursive relations between layers, the explicit piezothermoelastic solutions were deduced for functionally graded piezoelectric coatings on hollow spheres and circular cylinders.The solutions are accurate for multi-layered functionally graded piezoelectric coatings. If a continuous functionally graded piezoelectric coating was divided

to many layers,a approximate solution will be obtained and converged to the

 accurate solutions when the number of layers increased.Piezoelectric effects were ignorable on the stresses in substrate,

but very obvious on the stresses in coating.Increasing the number of layers

in coatings does not decrease the maximum stress,but obviously decreases

the jump of circumferencial stresses between layers and reduces interfacial

stress concentration.However,interfacial strenghth is weakened because the radial stress between coating and substrate increases with the number of layers. 

coating;

针对以球壳和圆柱壳为基体的功能梯度压电涂层,由多场耦合控制方程和层间连续条件导出递推关系,建立了显式的力-电-热多场耦合解。对于多层功能梯度压电涂层,此解为精确解;对于连续功能梯度压电涂层,可将涂层分为若干层,只要层数取得足够大,所得的近似解将收敛于精确解。研究表明:压电效应对基体的应力影响可以忽略,但对涂层的应力影响非常显著;增加层数并不能有效降低最大应力,但增加层数可显著减小相邻层层间周向应力的突变幅度,减小层间应力集中;然而涂层与基体之间的界面径向应力却随层数的增大而使界面强度弱化。

涂层, 压电, 功能梯度材料, 多场耦合, 热残余, 壳体