含固支边的压电层合板的解析解

ANALYTICAL SOLUTION FOR LAMINATED PIEZOELECTRIC PLATES WITH CLAMPED EDGES

  • 摘要: 首先由H-R(Hellinger-Reissner)变分原理简要地推导了压电材料的非齐次状态方程,然后通过引入边界应力函数,建立了含固支边压电层合板的非齐次状态方程,最后采用增维方法将非齐次状态方程转化成齐次状态方程。齐次方程方法不仅有利于程序的实现和数值运算稳定性,同时避免了矩阵求逆运算,大大地提高了计算效率。数值实例证明了该方法的正确性。

     

    Abstract: Firstly, the non-homogeneous state equation of piezoelectric materials was derived simply from H-R (Hellinger-Reissner) mixed variational principle in this paper. And then, non-homogeneous state equation for the laminated piezoelectric plates with clamped edges was established by assuming boundary stress function. Finally the non-homogeneous state equation was transformed into the homogeneous state equation by employing the dimensional expanding method. This homogeneous equation algorithm is not only benefit to programming and the numerical stability, but also the inverse matrix calculation is avoided, thus the computing efficiency is improved greatly. Numerical example shows that the method presented in this paper is correct.

     

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