压电智能结构有限变形下热-机耦合的有限元分析

FINITE ELEMENT ANALYSIS OF THERMO-MECHANICAL BEHAVIOUR OF PIEZOELCTRIC STRUCTURES UNDER FINITE DEFORMATION

采用有限元方法研究了结构在热载荷作用下变形与热传导之间的耦合特性。分析表明,结构变形较小,非线性效应很弱时,变形对材料的热传导系数影响很小,对结构的温度分布几乎没有影响;当变形增大,非线性效应增强时,变形对材料的热传导特性影响显著,热载荷作用下结构的温度变化和变形与现行不考虑热-机耦合效应所得结果产生明显差异。因此,为实现压电智能结构形状(振动)的精确控制,分析及实施控制时须考虑热-机耦合及变形对热传导系数的影响。

The governing equations of the piezoelectric structures are formulated through the theory of virtual displacement principle and a finite element method is developed. The fully coupled piezo-ther- mo-elastic behavior and the geometric non-linearity are considered in the finite element method. The method is then applied to simulate the dynamic and steady response of a clamped plate subjected to a heat flux acting on one side of the plate mimicking the behavior of a battery plate of satellite irradiated under the sun. The thermal conductivity of the plate is assumed to be deformation dependent in this study. The results obtained are compared against classical solutions, whereby the thermal conductivity is assumed to be independent of deformation. It is found that the full coupled theory predicts less transient response of the temperature compared to the classic analysis. In the steady state limit, the predicted temperature distribution within the plate for small heat flux is almost the same for both analysis. Howev- er, increasing the heat flux will increase the deviation between the predictions of the temperature distri- bution by the full coupled theory and that by classic analysis. The thermal conductivity is no longer a constant but shows noticeable dependence upon the deformation. It is concluded that, in order to predict the deformation of smart structures precisely, the piezo-thermo-elastic coupling, geometric non-linearity and the deformation dependent thermal conductivity must be taken into account.