轴向均布载荷下压杆稳定问题的DQ解

叙述了微分求积法(differential quadrature method)的一般方法，研究用微分求积法求解在均布轴向载荷下细长杆的稳定问题．通过Newton-Raphson法求解非线性方程组，以及对问题进行线性假设后求解广义特征值方程，得到了精度很高的后屈曲挠度数值和临界载荷数值．与解析解和其他近似解相比，微分求积法具有较高的精度和简便性．

THE DQ SOLUTION OF BUCKLING OF COLUMN UNDER AXIAL LOADING

In this paper, the differential quadrature method(DQM) is briefly described, and is used to deal with the problem of the buckling of a column under axial loading. The non-linear equations are solved by the Newton-Raphson method. And the generalized eigenvalue equation is solved under a linear hypothesis. We obtain the displacement at any position and the critical value at the bifurcation point. Numerical results show that the differential quadrature method possesses a higher accuracy and is easier to implement as compared with the analytic solution and other approximate solutions for the problem.