| Variation principle of piezothermoelastic bodies, canonical equation and homogeneous equation |
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| 作者姓名： | 刘继红 张惠明 |
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| 作者单位： | State Key Laboratory of Engines Tianjin University，State 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，Tianjin 300072，P.R.China |
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| 摘 要： | Combining the symplectic variations theory,the homogeneous control equa- tion 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 bod- ies was derived.Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered,and the non-homogeneous canoni- cal equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the inceusement 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 equa- tion 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.
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| 关 键 词： | 哈密顿原理 偶对 控制方程 弹性力学 |
| 收稿时间： | 2006-02-24 |
| 修稿时间： | 2006-07-14 |
Variation principle of piezothermoelastic bodies,canonical equation and homogeneous equation |
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| Liu Yan-hong,Zhang Hui-ming.Variation principle of piezothermoelastic bodies, canonical equation and homogeneous equation[J].Applied Mathematics and Mechanics(English Edition),2007,28(2):193-200. |
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| Authors: | Liu Yan-hong Zhang Hui-ming |
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| Institution: | 1. State 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
2. State Key Laboratory of Engines, Tianjin University, Tianjin 300072, P. R. China |
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| Abstract: | Combining the symplectic variations theory,the homogeneous control equa- tion 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 bod- ies was derived.Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered,and the non-homogeneous canoni- cal equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the inceusement 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 equa- tion 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. |
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| Keywords: | piezothermoelasticity Hamilton principle Hamilton canonical equation symplectic variables homogeneous equation homogeneous isoparametric element formulations |
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