【摘要】 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.更多还原

【Abstract】 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.更多还原