用摄动-加权残值联合法求解圆板大挠度问题

Hybrid Methods of Perturbation - Weighted Residual for the Large Deflection of a Circular

本文采用摄动-加权残值联合法求解圆板大挠度问题。文中先用正则摄动法求得摄动展开中的各阶函数,然后以此函数作为试函数,采用加权残值法计算待定系数,从而得出其近似解。文中给出了均布荷载作用下周边固支圆板的算例,结果表明,其结果与摄动解相比具有更高的精度。

In this paper a hybrid perturbation - weighted residual method is proposed for the large deflection of a circular. First,an orthogonal method is used to get the perturbation into a series of functions. Then,a weighted residual method is applied to calculate the coefficients of the function series, and thus to obtain the approximate solution. Finally,an example of a round supported circular under uniform load is given. The example shows that the solution is more accurate than that of the perturbation method.