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为了精确求解复合受载下简支矩形板屈曲失稳的问题。推导简支矩形板无量纲屈曲微分方程,给出简支矩形板屈曲分析的微分求积计算格式。以单(双)向轴压作用下的简支矩形板为例,通过与解析解、有限元解对比验证微分求积法求解简支矩形板屈曲失稳问题的精确性。以轴压和剪应力作用下的简支矩形板为例,通过同解析解对比分析表明,当边长比r=1～5时,解析解与数值解间的差别较小;当边长比r=1/5～1时,解析解随方程数N的增大而逐步逼近数值解。
In order to solve the problem of buckling instability of simply supported rectangular plate subjected to composite loading. The dimensionless buckling differential equation of simply supported rectangular plate is deduced, and the differential quadrature format of buckling analysis of simply supported rectangular plate is given. Taking the single (double) simple supported rectangular plate subjected to axial compression as an example, the accuracy of the buckling problem of simply supported rectangular plate subjected to differential quadrature method was verified by comparison with analytical solution and finite element method. Taking the simply supported rectangular plate subjected to axial compression and shear stress as an example, the comparative analysis of analytical solution shows that the difference between analytical solution and numerical solution is small when the ratio of side length to length is from 1 to 5. When the side length ratio When r = 1/5 ~ 1, the analytical solution gradually approximates the numerical solution as the number of equations N increases.