| 升阶试函数族在矩形板大挠度问题中的应用 |
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| 引用本文： | 李辉荣.升阶试函数族在矩形板大挠度问题中的应用[J].力学与实践,2004,26(3):47-50. |
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| 作者姓名： | 李辉荣 |
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| 作者单位： | 西南石油学院机电工程学院,成都,610500 |
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| 摘 要： | 为解决加权残值法求近似解的计算精度问题，将摄动法与加权残值法相结合，首先以板中心挠度为摄动参数进行摄动，将矩形板大挠度非线性偏微分方程组分解为线性偏微分方程组，然后用最小二乘法求解．求解中构造并应用了可以由控制参数，调节的升阶试函数族，计算结果与实验结果基本一致，与以前的研究比较，计算精度明显提高．该方法对于寻求最佳试函数和最佳近似值是一种有效的方法．
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| 关 键 词： | 升阶试函数族 矩形板 大挠度 摄动法 加权残值法 最小二乘法 |
| 修稿时间： | 2003年1月16日 |
A NEW TYPE OF TRIAL FUNCTIONS IN APPLICATIONS TO THE SOLUTION OF LARGE DEFLECTION PERTURBATION EQUATIONS FOR RECTANGULAR PLATES |
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| LI Huirong.A NEW TYPE OF TRIAL FUNCTIONS IN APPLICATIONS TO THE SOLUTION OF LARGE DEFLECTION PERTURBATION EQUATIONS FOR RECTANGULAR PLATES[J].Mechanics and Engineering,2004,26(3):47-50. |
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| Authors: | LI Huirong |
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| Institution: | LI Huirong Department of Mechanical Engineering,Southwest Petroleum Institute,Chengdu 610500,China |
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| Abstract: | To obtain an approximate solution with the
method of weighted residuals, the perturbation method
with plate center deflection as perturbation parameter is
used to turn nonlinear partial differential equations for
large deflection of rectangular plate to linear partial dif-
ferential equations. Then. a solution is obtained with the
least square method. In the course of solution, an as-
cending power trial function family is used, which can be
conditioned by the control parameter f. The results agree
with the experimental ones. Compared with previous re-
searches, the precision of calculation is improved evidently.
It is an effective method to obtain a best trial function and
a best approximate value. |
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| Keywords: | rectangular plate large deflection perturbation method weighted residul method trail function |
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