压电热弹性体的变分原理及正则方程和齐次方程

刘艳红; 张惠明

压电热弹性体的变分原理及正则方程和齐次方程

刘艳红^1,2,
张惠明¹

1.
天津大学内燃机燃烧学国家重点实验室,天津 300072;
中国民航大学机电分院,天津 300300

基金项目: 国家自然科学基金资助项目(50276041)

详细信息

作者简介:
刘艳红(1970- ),女,河南人,副教授,博士生(联系人.Tel:+86-22-24093144;E-mail:lyhqzh@126.com).

中图分类号: O343.2；O176
计量
- 文章访问数: 2739
- HTML全文浏览量: 92
- PDF下载量: 644
- 被引次数: 0
出版历程
- 收稿日期: 2006-02-24
- 修回日期: 2006-07-14
- 刊出日期: 2007-02-15

Variation Principle of Piezothermoelastic Bodies,Canonical Equation and Homogeneous Equation

LIU Yan-hong^1,2,
ZHANG Hui-ming¹

1.
Stat Key Laboratory of Engines, Tianjin University, Tianjin 300072, P. R. China;
Aeronautical Mechanics and Avionics Engineering College, Civil Aviation University of China, Tianjin 300300, P. R. China

摘要

摘要: 结合对偶变量理论，为压电热弹性体混合层合板问题推导了齐次的控制方程和Hamilton等参元列式．首先根据广义的Hamilton变分原理推导了压电热弹性体非齐次的Hamilton正则方程．然后进一步考虑了热平衡方程与导热方程中变量的对偶关系，通过增加正则方程的维数，成功地将非齐次的正则方程转化为能独立求解压电热弹性体耦合问题的齐次控制方程．为了推导四节点Hamilton等参元列式的方便，可将温度梯度关系类比成本构关系并构建新的变分原理．齐次方程大大简化了人们在分析压电热弹性体耦合问题时，通常要求解非齐次方程和关于平衡方程和导热方程的二阶微分方程的繁琐方法，同时也减少了数值计算工作量．
- 压电热弹性体 /
- Hamilton原理 /
- Hamilton正则方程 /
- 对偶变量 /
- 齐次方程 /
- 等参元齐次列式
Abstract: Combining the symplectic variations theory,the homogeneous control equation and isoparametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced.Firstly,based on the generalized Hamilton variation principle,the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived.Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered.The non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation.For the convenience of deriving Hamilton isoparametric element formulations with four nodes,one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle.The homogeneous equation simplifies greatly the solution programs which are often performed to solve non-homogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.
- piezothermoelasticity /
- Hamilton principle /
- Hamilton canonical equation /
- symplectic variables /
- homogeneous equation /
- homogeneous isoparametric element formulation

HTML全文

参考文献(16)

[1]	Pagano N J. Exact solutions for rectangular bidirectional composites and sandwich plates[J].Journal of Composite Materials,1970,4(1):20-34.
[2]	Ray M C, Rao K M, Samanta B. Exact solution for static analysis of an intelligent structure under cylindrical bending[J].Computers and Structures,1993, 47(6):1031-1042. doi: 10.1016/0045-7949(93)90307-Y
[3]	Batra R C, Liang X Q. Vibration of a rectangular laminated elastic plate with embedded piezoelectric sensors and actuators[J].Computer and Structures,1997,63(2):203-216. doi: 10.1016/S0045-7949(96)00349-5
[4]	Ray M C, Bhattacharya R, Samanta B. Exact solutions for dynamic analysis of composite plate with distributed piezoelectric layers[J].Compute and Structures,1998,66(6):737-743. doi: 10.1016/S0045-7949(97)00126-0
[5]	Vel S S, Batra R C. Generalized plane strain thermopiezoelectric analysis of multilayered plates[J].Journal of Thermal Stresses,2003,26(4):353-377. doi: 10.1080/713855902
[6]	Heyliger P R, Brooks P. Exact solution for laminated piezoelectric plates in cylindrical bending[J].Journal of Applied Mechanics,1996,63(6):903-910. doi: 10.1115/1.2787245
[7]	Xu K, Noor A K, Tang Y Y.Three-dimensional solutions for coupled thermoelectroelastic response of multilayered plates[J].Computer Methods in Applied Mechanics and Engineering,1995,126(3/4):355-371. doi: 10.1016/0045-7825(95)00825-L
[8]	Ootao Y, Tanigawa Y.Control of transient thermoelastic displacement of a two-layered composite plate constructed of isotropic elastic and piezoelectric layers due to nonuniform heating[J].Archive of Applied Mechanics,2001,71(4/5):207-230. doi: 10.1007/s004190000136
[9]	Tran Jiann-quo. A state space formalism for piezothermoelasticity[J].International Journal of Solids and Structures,2002,39(20):5173-5184. doi: 10.1016/S0020-7683(02)00413-4
[10]	Kapuria S, Dumir P C,Sengupta S.Three-dimensional solution for shape control of a simply supported rectangular hybrid plate[J].Journal of Thermal Stresses,2003,22(2):159-176.
[11]	Zhang C, Cheung Y K,Di S,et al.The exact solution of coupled thermoelectroelastic behavior of piezoelectric laminates[J].Computers and Structures,2002,80(13):1201-1212. doi: 10.1016/S0045-7949(02)00060-3
[12]	Ding H J, Wang H M, Ling D S. Analytical solution of a pyroelectric hollow cylinder for piezothermoelastic axisymmetric dynamic problems[J].Journal of Thermal Stresses,2003,26(3):261-276. doi: 10.1080/713855893
[13]	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.
[14]	钟万勰. 应用力学对偶体系[M].北京：科学出版社，2003.
[15]	卿光辉, 邱家俊,刘艳红.磁电弹性体修正后的H-R混合变分原理和状态向量方程[J].应用数学和力学,2005,26(6)：665-670.
[16]	顾元宪, 陈飚松,张洪武.结构动力方程的增维精细积分法[J].力学学报，2000,32(4)：447-456.