热载荷下压电复合板有限元建模与形变控制

热载荷是引起在轨空间结构形变的重要因素之一，采用压电材料对结构热变形进行主动补 偿，需要建立热、电、力场相互耦合的动力学模型. 基于高阶位移场、高阶电势分布和线性 温度模型，推导了压电复合板结构的热、电、力场耦合的高阶有限元模型. 通过对压电双晶 片梁的分析，得到了压电片中电势沿厚度方向的抛物线型分布，而非通常文献中假设的线性 化分布模型的结果. 针对表面粘贴压电片的压电复合板，计算了热载荷作用下压电复合板的变形、 传感器的电压以及主动补偿后的结构变形，与文献给出的结果基本一致，验证了模型的正 确性. 同时还指出热电效应对结构变形和传感器电压具有十分重要的影响.

FINITE ELEMENT MODELLING AND SHAPE CONTROL FOR PIEZOELECTRIC COMPOSITE PLATES UNDER THERMAL LOAD

The deformation induced by thermal loads in flexible space structures may be actively compen- sated using piezoelectric materials.In order to develop the finite element formulations coupled with thermo- mechanical-electric effects,the refined higher order displacement field,the high order electrical potential field and the linear temperature field were adopted.The numerical examples of the piezoelectric bimorph beam and composite plate were taken.The parabolic through-thickness distribution of electric potential at the middle of the beam is found by the present model,which is different from the linear distribution assumption.Numerical examples show that the present model can well predict the thermal deformation with or without active com- pensation and the voltage of sensor,all in good agreement with those from literature.The pyroelectric effects may influence the structural deflection and sensor's voltage significantly.