GDQR求解变截面圆拱的屈曲问题

给出了两端不可压缩变截面拱的屈曲方程，用广义微分求积法则(GDQR)分析了不变截面拱的屈曲问题后，又将该方法引伸到另外三种变截面圆拱的屈曲问题，求出了在三类边界条件下第一类和第二类稳定性的屈曲荷载．求解过程中，使用了Lagrange和Chebyshev两种权系数矩阵，并作比较．结果表明，用GDQR求解不变截面或变截面屈曲问题时，方法简单，易于理解且精度高．使用这两种权系数，求解Chebyshev权系数时要用到符号编程，比较耗时，但是该方法相对Lagrange法收敛性要好．

In-plane buckling analysis of non-uniform circular arches by the generalized differential quadrature rule

This paper brings two classical methods to get the coefficient s matrices of the generalized differential quadrature rule (GDQR): Lagrange and Chebyshev polynormials, then it gives the buckling equation of non-uniform circu lar arches with two ends uncompressible. After analyzed the buckling of uniform circular arches by GDQR, the buckling of three kinds of sections are emphasized. what's more, the first and second buckling loads are also analyzed with three d ifferent boundary conditions. During the analyzing, the above Lagrange and Cheby shev coefficients are always in use; in addition they are also compared. In conc lusion, it's very easy and feasible to solve non-uniform circular arches by GDQR , and the results are very good. It's more difficult to get Chebyshev coefficien ts when obtaining the coefficients matrices, but Chebyshev coefficients are bett er than the Lagrange in convergence.