In this paper, we analyze the hygro-thermo-electro-mechanical (HTEM) coupling problem of functionally graded piezoelectric (FGPE) structure based on edge-based smoothed point interpolation method (ES-PIM). The basic equations for FGPE structure are derived in the multi-physical field. Triangular elements adopted in ES-PIM can be generated automatically and suitable for complicated structures. The responses for the HTEM coupling problem are calculated by ES-PIM and finite element method (FEM) under different hygrothermal conditions. Through the numerical examples, the factors related to the temperature and moisture fields are explored. The exponential factor and the hygrothermal effect on the responses of the FGPE structure are also studied. Besides, the advantages of proposed method for HTEM coupling problems are also validated by several numerical examples. These solutions also indicate that the increase of temperature and moisture concentration decreases the structural stiffness when empirical constants are set to negative numbers, leading to the decrease of frequency and variation of displacement. This article proposes an excellent numerical method and provides a reference for the design and application of piezoelectric structures.

在本文中，我们基于基于边缘的平滑点插值方法（ES-PIM）分析了功能梯度压电（FGPE）结构的湿热电机械（HTEM）耦合问题。FGPE结构的基本方程式是在多物理场中得出的。ES-PIM中采用的三角元素可以自动生成，并适合复杂的结构。通过ES-PIM和有限元方法（FEM）在不同的湿热条件下计算HTEM耦合问题的响应。通过数值算例，探讨了与温度和湿度场有关的因素。还研究了指数因子和湿热效应对FGPE结构响应的影响。除了，几个数值算例也验证了所提出的解决HTEM耦合问题的方法的优点。这些解决方案还表明，当经验常数设置为负数时，温度和水分浓度的增加会降低结构刚度，从而导致频率降低和位移变化。本文提出了一种很好的数值方法，为压电结构的设计和应用提供了参考。