Unlike the widely used eigen-buckling theory, the nonlinear post-buckling analysis provides a more accurate stability model of piezoelectric cylindrical shells and predicates more reliable instability characteristics. In this paper, an accurate post-buckling analysis of piezoelectric functionally graded cylindrical shells under combined electro-thermo-mechanical loadings is performed. The nonlinear large deflection governing equations involving the self-induced electric potential are established based on the higher-order shear deformation theory. The post-buckling equilibrium paths with mode-jumping phenomenon for both symmetric and asymmetric deformation modes are obtained by the Galerkin's method enriched with new displacement functions. Results indicate that the symmetric mode usually occurs for a thick shell and the asymmetric mode only occurs for an ultrathin shell. Furthermore, it is demonstrated that the effect of power law index highly depends on the external electro-thermal loadings. Therefore, the loading capacity of the piezoelectric FG cylindrical shells can be improved by an appropriately selected power law index.

与广泛使用的本征屈曲理论不同，非线性后屈曲分析提供了更准确的压电圆柱壳稳定性模型，并预测了更可靠的不稳定特性。在本文中，在电-热-机械联合载荷下对压电功能梯度圆柱壳进行了精确的后屈曲分析。基于高阶剪切变形理论建立了涉及自感电位的非线性大挠度控制方程。对称和非对称变形模式具有模式跳跃现象的后屈曲平衡路径是通过丰富了新位移函数的伽辽金方法获得的。结果表明，对称模式通常发生在厚壳上，非对称模式只发生在超薄壳上。此外，证明了幂律指数的影响高度依赖于外部电热载荷。Therefore, the loading capacity of the piezoelectric FG cylindrical shells can be improved by an appropriately selected power law index.