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 引用本文: 李尧臣 亓峰 仲政. 功能梯度压电材料圆板的简化理论与解析解[J]. 力学学报, 2008, 40(5): 636-645.
Yaochen Li, Feng Qi, Zheng Zhong. Simplified theory and analytical solutions for functionally graded piezoelectric circular plate[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(5): 636-645.
 Citation: Yaochen Li, Feng Qi, Zheng Zhong. Simplified theory and analytical solutions for functionally graded piezoelectric circular plate[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(5): 636-645.

Simplified theory and analytical solutions for functionally graded piezoelectric circular plate

• 摘要: 提出了功能梯度圆板在轴对称载荷作用下的简化理论与解析解. 引入了板理论的若干假设(Kirchhoff假设的一部分，Reissner-Mindlin假设和文中提出的假设)，并假设材料常数在板厚方向按指数规律变化. 推导了板的周边固定或简支同时又接地情况下中性层法线转角的解和用Fourier-Bessel级数表示的电势解. 这个解在形式上比精确解简单得多，进行数值计算时也相当方便与快捷. 该文给出了板的周边固定、接地情况下的计算结果并进行了讨论，对于理论和方法的正确性作了验证.

Abstract: Simplified theory and analytical solutions for afunctionally graded piezoelectric circular plate subjected to axisymmetricloading was presented with some assumptions, such as Kirchhoff assumption,Reissner-Mindlin assumption, and the assumption that material propertiesvary exponentially across the thickness of the plate. We derived thesolution of the rotation angle of the normal line of the neutral layer andthe solution of the electric potential in the plate expressed byFourier-Bessel series, in the cases that the edges of the plate was fixed orsimply supported and grounded. The presented solutions were obviously simplecompared with some exact analytical solutions and easy to perform thenumerical analysis. The numerical results for the edge-fixed/grounded platewere applied to validate the simplified theory presented in the paper.

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