关于平板屈曲重调和特征值问题的H^2协调谱元法

The H^2-conforming spectral element method for the biharmonic eigenvalue problem of plate buckling

通过使用H^2协调谱元法,具体求解了平板屈曲重调和特征值问题。首先给出H^2协调谱元法的误差估计,然后利用广义雅可比多项式和节点基函数构造二维谱元空间的基函数,最后报道了L形区域和方形区域上的数值实验,实验结果表明谱元法所计算的特征值受网格直径和多项式次数的影响,在区域选择上较谱方法更为灵活,适用于平板屈曲重调和特征值问题。

By using H^2-conforming spectral element method,the biharmonic eigenvalue problem of plate buckling is solved. Firstly,the error estimates of H^2-conforming spectral element method are given. Then a set of basis functions on the two-dimensional spectral element space is constructed by generalized Jacobi polynomials and nodal basis functions. Finally,the numerical experiments are carried out on the L-shaped domain and the square domain. The experimental results show that eigenvalues obtained by spectral element method are affected by grid diameter and degree of polynomial. The spectral element method is more flexible in domain than spectral method and is applicable to the biharmonic eigenvalue problem of plate buckling.