Finite element analysis of thermoelastic behavior of piezoelectric structures under finite deformation

It is noted that the behavior of most piezoelectric materials is temperature dependent and such piezo-thermo-elastic coupling phenomenon has become even more pronounced in the case of finite deformation. On the other hand, for the purpose of precise shape and vibration control of piezoelectric smart structures, their deformation under external excitation must be ideally modeled. This demands a thorough study of the coupled piezo-thermo-elastic response under finite deformation. In this study, the governing equations of piezoelectric structures are formulated through the theory of virtual displacement principle and a finite element method is developed. It should be emphasized that in the finite element method the fully coupled piezo-thermo-elastic behavior and the geometric non-linearity are considered. The method developed is then applied to simulate the dynamic and steady response of a clamped plate to heat flux acting on one side of the plate to mimic the behavior of a battery plate of satellite irradiated under the sun. 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 analyses. However, it is noted that increasing the heat flux will increase the deviation between the predictions of the temperature distribution by the full coupled theory and by the classic analysis. It is concluded from the present study that, in order to precisely predict the deformation of smart structures, the piezo-thermo-elastic coupling, geometric non-linearity and the deformation dependent thermal conductivity should be taken into account.