LIU Yan-hong, ZHANG Hui-ming. Variation Principle of Piezothermoelastic Bodies,Canonical Equation and Homogeneous Equation[J]. Applied Mathematics and Mechanics, 2007, 28(2): 176-182.
 Citation: LIU Yan-hong, ZHANG Hui-ming. Variation Principle of Piezothermoelastic Bodies,Canonical Equation and Homogeneous Equation[J]. Applied Mathematics and Mechanics, 2007, 28(2): 176-182.

# Variation Principle of Piezothermoelastic Bodies,Canonical Equation and Homogeneous Equation

• Rev Recd Date: 2006-07-14
• Publish Date: 2007-02-15
• 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.
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