To accurately simulate the steady-state responses of a functionally graded piezoelectric structure (FGPS) and cure the “overly-stiff” of finite element method (FEM), the coupled thermal-electrical-mechanical inhomogeneous cell-based smoothed finite element method (CICS-FEM) is proposed. The gradient smoothing technique is introduced into FEM and a “close-to-exact” stiffness is obtained. Based on the basic theory of FGPS, the thermal field is introduced into the electrical-mechanical coupling field and the multi-physics coupling equations are given in conjunction with the cell-based smoothed finite element method. CICS-FEM is verified with several examples, and there is a satisfactory agreement between the current solution and the reference solution. Therefore, the developed method to solve the steady-state response of FGPS can provide a reference for the design and manufacture of smart devices.

中文翻译：

---

基于耦合热-电-机非均匀单元的平滑有限元法 (CICS-FEM) 的功能梯度压电结构的稳态响应

为了准确模拟功能梯度压电结构 (FGPS) 的稳态响应并解决有限元法 (FEM) 的“过硬”问题，采用耦合的热-机电-机械非均匀单元平滑有限元法 (CICS) -FEM) 被提议。梯度平滑技术被引入 FEM 并获得“接近精确”的刚度。基于FGPS的基本理论，将热场引入机电耦合场，结合基于单元的平滑有限元法，给出了多物理场耦合方程。CICS-FEM 用几个例子进行了验证，当前解决方案与参考解决方案之间有一个令人满意的一致性。所以，