Coupled Thermal-electrical-mechanical Inhomogeneous Cell-based Smoothed Finite Element Method For Functionally Graded Piezoelectric Materials

The rapid development of science and technology has made the application of smart materials more and more widely in practical engineering.Among them,functionally graded piezoelectric materials have attracted the attention of researchers at home and abroad because of their good force-electric coupling and inhomogeneous characteristics.As the core of smart devices,functionally graded piezoelectric materials are often exposed to high-temperature operations.The interaction of force field,electric field and thermal field makes it more difficult to solve the response of functionally graded piezoelectric structures.In practical engineering,the finite element method is by far the most mature and most widely used numerical calculation method for solving multi-physics coupling problems,but the stiffness matrix it constructs is "hard" and requires high mesh quality.The smoothed finite element method is based on the Gaussian divergence theorem,which converts volume integrals / area integrals into area integrals / line integrals and eliminates the step of deriving shape functions,simplifying the calculation process.This method has low requirements on mesh quality,high calculation accuracy and has been favored by many scholars.Based on the basic equations of functionally graded piezoelectric materials and finite element methods,the smoothing strain technology is introduced.Then,a coupled thermal-electrical-mechanical cell-based smoothed finite element method(CICS-FEM)is proposed.The governing equations of CICS-FEM,combined with the modified Wilson-? method,are used to solve the steady-state / transient response of functionally graded piezoelectric materials in thermal-electrical-mechanical coupling.The feasibility and effectiveness of CICS-FEM is verified by numerical calculation of functionally graded piezoelectric structures.The results obtained by using the traditional finite element method with increased density meshes as reference solutions are compared with the results obtained by CICS-FEM,then,the advantages of CICS-FEM are obtained.The results of numerical examples show that CICS-FEM effectively solves the problems of ‘over-stiff' of the finite element method stiffness matrix,small displacement solutions,high mesh quality requirements and low ability to deal with distorted meshes.It has the characteristics of high convergence,high accuracy and high efficiency.