Modified H-R Mixed Variational Principle for Magnetoelectroelastic Bodies and State-Vector Equation

QING Guang-hui; QIU Jia-jun; LIU Yan-hong

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2005 > 26(6): 665-670

QING Guang-hui, QIU Jia-jun, LIU Yan-hong. Modified H-R Mixed Variational Principle for Magnetoelectroelastic Bodies and State-Vector Equation[J]. Applied Mathematics and Mechanics, 2005, 26(6): 665-670.

Citation:

PDF( 257 KB)

Modified H-R Mixed Variational Principle for Magnetoelectroelastic Bodies and State-Vector Equation

1.
Aeronautical Mechanics & Avionics Engineering College, Civil Aviation University of China, Tianjin 300300, P. R. China;

Received Date: 2004-05-08
Rev Recd Date: 2005-01-25
Publish Date: 2005-06-15

Abstract

Abstract

Based upon the Hellinger-Reissner(H-R) mixed variational principle for three-dimensional elastic bodies,the modified H-R mixed variational theorem for magnetoelectroelastic bodies was established.The state-vector equation of magnetoelectroelastic plates was derived from the proposed theorem by performing the variational operations.To lay a theoretical basis of the semi-analytical solution applied with the magnetoelectroelastic plates,the state-vector equation for the discrete element in plane was proposed through the use of the proposed principle.Finally,it is pointed out that the modified H-R mixed variational principle for pure elastic,single piezoelectric or single piezomagnetic bodies are the special cases of the present variational theorem.
- magnetoelectroelastic body,
- variational principle,
- laminated plates,
- state-vector equation,
- semi-analytical solution

FullText(HTML)

References(11)

References

[1]	刘金喜，王祥琴，王彪.横观各向同性电磁弹性固体耦合方程的一般解[J].应用数学和力学，2003,24(7):684—690.
[2]	丁皓江，江爱民.横观各向同性磁电弹性体的基本解和边界积分方程[J].中国科学，E辑，2003，33(9)：845—855.
[3]	WANG Jian-guo,FANG Shi-sheng,CHEN Lin-feng.State vector approach to analysis of multilayered magneto-electro-elastic plates[J].International Journal of Solids and Structures,2003,40(7):1669—1680. doi: 10.1016/S0020-7683(03)00027-1
[4]	Pan E.Exact solution for simply supported and multilayered magneto-electro-elastic plates[J].Journal of Applied Mechanics,2001,68(4):608—618. doi: 10.1115/1.1380385
[5]	Pan E,Heyliger P.Free vibrations of simply supported and multilayered magneto-electro-elastic plates[J].Journal of Sound and Vibration,2002,252(3):429—442. doi: 10.1006/jsvi.2001.3693
[6]	唐立民,褚致中,邹贵平，等.混合状态Hamiltonian元的半解析解和叠层板的计算[J].计算结构力学及其应用,1992,9(4):347—360.
[7]	欧阳华江,钟万勰,杨琦，等.一类基于Hamilton体系的半解析法[J].计算结构力学及其应用,1993,10(2):129—136.
[8]	姚伟岸.电磁弹性固体三维问题的广义变分原理[J].计算力学学报,2003,20(4):487—489.
[9]	Reissner E.On a variational theorem in elasticity[J].Journal of Mathematics and Physics,1950,29(1):90—95.
[10]	钟万勰.弹性力学求解新体系[M].大连:大连理工大学出版社,1995,155—159.
[11]	Steele C R,Kim Y Y.Modified mixed variational principle and the state-vector equation for elastic bodies and shells of revolution[J].Journal of Applied Mechanics,1992,59(3):587—595. doi: 10.1115/1.2893764