功能梯度热释电材料矩形板的三维精确分析

对四边简支、接地、等温的功能梯度热释电材料矩形板进行精确三维分析．根据正交各向异性热释电材料基本方程，导出了功能梯度热释电材料的状态方程．假定材料的机械、电学和热学性质沿板厚方向按统一的指数函数形式梯度分布，获得了四边简支、接地和等温的矩形板，在上下表面作用任意的机械荷载、电荷载和热荷载情况下的三维精确解．通过算例，分析了在机械荷载、电荷载和热荷载分别作用下，材料性质的不同梯度变化对平板结构响应的影响．所获得的精确结果可作为评价其他近似方法的标准解答或者作为建立简化的功能梯度热释电材料平板理论的基础。

THREE DIMENSIONAL EXACT ANALYSIS OF FUNCTIONALLY GRADIENT PIEZOTHERMOELECTRIC MATERIAL RECTANGULAR PLATE

This paper presented an exact three-dimensional analysis for a functionally gradient piezothermoelectric material rectangular plate that is simply supported, grounded and isothermal along its four edges. The state equations of the functionally gradient piezothermoelectric material were developed based on the basic equations of anisotropic piezothermoelectric materials. Assuming that the mechanical, electric and thermal properties of the material have the same exponential law dependence on the thickness-coordinate, we obtained an exact three-dimensional solution of a simply supported, grounded and isothermal rectangular plate under arbitrary mechanical, electric and thermal loading on the top and bottom surfaces. The influence of different functionally gradient material properties on the structural response of the plate to the mechanical, electric and thermal stimuli was studied through examples. The obtained exact solution could serve as a benchmark result to assess other approximate methodologies or as a basis for establishing simplified functionally gradient piezothermoelectric material plate theories.