非均布载荷作用下矩形板失稳的计算方法研究

Study on calculation method of instability of rectangular plate under non-uniform load

为了快速准确求解计算加劲箱梁腹板结构中局部矩形板的屈曲承载力,基于微分求积方法获取非均布载荷作用下矩形板的屈曲承载能力,对传统计算方法中的经验设计公式进行了修正。首先,推导了非均布载荷作用下简支矩形板无量纲屈曲控制微分方程的微分求积计算格式,经与文献解对比验证了微分求积数值解的精确性;其次,建立了包含非均布载荷系数与边长比的参数分析案例矩阵,并给出了传统计算方法解与数值解之间的相对误差值,找出相对误差较大的边长比参数区间;同时,通过离散系数分析评价了不同边长比对应屈曲失稳系数之间的离散程度,找出离散系数小时所对应的非均布载荷参数区间;最后,针对离散系数小时所对应的非均布载荷参数区间,选取边长比参数区间对应所有屈曲失稳系数中的最小值,拟合提出了非均布载荷系数与屈曲失稳系数最小值之间的修正计算方法,并将修正计算方法解、传统计算方法解与数值解进行对比分析验证。研究结果表明:提出的微分求积法数值分析模型求解精度高;以拉为主的非均布载荷系数,传统计算方法解与数值解之间相对误差区间为[-26.65%,-88.99%],不同边长比对应屈曲失稳载荷之间的离散系数区间为[0.18, 0.767]×10^(-3),拟合修正计算方法时可忽略边长比变化对屈曲失稳载荷的影响;修正计算方法解与数值解之间吻合度较好。

To quickly and accurately calculate the buckling bearing capacity of rectangular plates in the web of stiffening box,the buckling bearing capacity of rectangular plates under non-uniformly distributed load was obtained by differential quadrature method,and the empirical design formula in the traditional calculation method was modified.Firstly,the differential quadrature calculation format of the dimensionless buckling control differential equation of simply supported rectangular plate under non-uniform load was derived,and the accuracy of the numerical solution of differential quadrature was verified by comparing with solutions in literature;secondly,the case matrix of parameter analysis including nonuniformly distributed load coefficient and side length ratio is established,and the relative error value between the traditional calculation method solution and the numerical solution were given,and the parameter interval of side length ratio with large relative error was found;thirdly,the dispersion degree between buckling instability coefficients corresponding to different side-to-side ratios was evaluated by discrete coefficient analysis,and the parameter interval of non-uniformly distributed load corresponding to small dispersion coefficient was found out;finally,for the parameter interval of non-uniformly distributed load corresponding to small discrete coefficient,the minimum value of all buckling instability coefficients corresponding to the parameter interval of side length ratio was selected,and a revised calculation method for the minimum values of nonuniformly distributed load coefficient and buckling instability coefficient was proposed through fitting,and the solution of this revised calculation method,traditional calculation method and numerical solution were compared and verified.Results show that the accuracy of numerical analysis model of differential quadrature method was high.The relative error range between the traditional calculation method and the numerical solution was[-26.65%,-88.99%],and the discrete coefficient range between different side-length ratios corresponding to buckling instability loads was[0.18,0.767]×10^(-3),so the influence of the change of side-length ratio on buckling instability loads can be ignored during the fitting of the modified calculation method.The solution of the modified calculation method is in good agreement with the numerical solution.