轴向均布载荷下压杆稳定问题的DQ解

THE DQ SOLUTION OF BUCKLING OF COLUMN UNDER AXIAL LOADING

  • 摘要: 叙述了微分求积法(differential quadraturemethod)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.

     

    Abstract: In this paper, the differential quadrature method(DQM) is briefly described, and is used to deal with the problem of thebuckling of a column under axial loading. The non-linearequations are solved by the Newton-Raphson method. And the generalizedeigenvalue equation is solved under a linearhypothesis. We obtain the displacement at anyposition and the critical value at the bifurcation point. Numerical resultsshow that the differential quadrature method possesses a higher accuracy andis easier to implement as compared with the analytic solution and other approximatesolutions for the problem.

     

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