A Three-Dimensional Size-Dependent Layered Model for Simply-Supported and Functionally Graded Magnetoelectroelastic Plates  

作　　者：Junhong Guo Jiangyi Chen Ernian Pan 

机构地区：[1]Department of Mechanics, Inner Mongolia University of Technology, Hohhot 010051, China [2]School of Mechanical Engineering, Zhengzhou University, Zhengzhou 450001, China [3]Department of Civil Engineering and Department of Mathematics, The University of Akron, Akron, OH 44325-3905, USA

出　　处：《Acta Mechanica Solida Sinica》2018年第5期652-671,共20页固体力学学报（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China （Grant Nos. 11262012, 11502123, 11172273） and the Natural Science Foundation of Inner Mongolia Autonomous Region of China （Grant No. 2015JQ01）.

摘　　要：A three-dimensional size-dependent layered model for simply-supported and func- tionally graded magnetoelectroelastic plates is presented based on the modified couple-stress theory. The functionally graded material is assumed to be exponential in the thickness direc- tion of the plate. The final governing equations are reduced to an eigensystem by expressing the extended displacements in terms of two-dimensional Fourier series. Using the propagator matrix method, the exact solutions of the magnetic, electric and mechanical fields of sandwich nanoplates with couple-stress effect and under the surface loads are derived. Numerical examples for two functionally graded sandwich plates made of piezoelectric BaTiO3 and magnetostrictive CoFe2O4 materials are presented to demonstrate the effect of the functional gradient factor and material length-scale parameter on the induced fields. The exact solutions presented in this work can also serve as benchmarks to various numerical methods for analyzing the size-dependent features in layered systems.A three-dimensional size-dependent layered model for simply-supported and func- tionally graded magnetoelectroelastic plates is presented based on the modified couple-stress theory. The functionally graded material is assumed to be exponential in the thickness direc- tion of the plate. The final governing equations are reduced to an eigensystem by expressing the extended displacements in terms of two-dimensional Fourier series. Using the propagator matrix method, the exact solutions of the magnetic, electric and mechanical fields of sandwich nanoplates with couple-stress effect and under the surface loads are derived. Numerical examples for two functionally graded sandwich plates made of piezoelectric BaTiO3 and magnetostrictive CoFe2O4 materials are presented to demonstrate the effect of the functional gradient factor and material length-scale parameter on the induced fields. The exact solutions presented in this work can also serve as benchmarks to various numerical methods for analyzing the size-dependent features in layered systems.

关 键 词：Functionally graded MAGNETOELECTROELASTIC Modified couple stress Layered plate Three-dimensional solution 

分 类 号：O151.21[理学—数学] P194.9[理学—基础数学]