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力学与实践 ›› 2004, Vol. 26 ›› Issue (3): 0-0.doi: 10.6052/1000-0992-2003-130

• 应用研究 •    

升阶试函数族在矩形板大挠度问题中的应用

李辉荣   

  1. 西南石油学院机电工程学院 成都 610500
  • 收稿日期:2003-01-11 修回日期:2003-08-15 出版日期:2004-06-10 发布日期:2004-06-10

A NEW TYPE OF TRIAL FUNCTIONS IN APPLICATIONS TO THE SOLUTION OF LARGE DEFLECTION PERTURBATION EQUATIONS FOR RECTANGULAR PLATES

  • Received:2003-01-11 Revised:2003-08-15 Online:2004-06-10 Published:2004-06-10

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$f$ 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.

关键词: 矩形板,大挠度,摄动法,加权残值法, 升阶试函数族

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 differential equations. Then, a solution is obtained with the least square method. In the course of solution, an ascending 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 researches, the precision of calculation is improved evidently. It is an effective method to obtain a best trial function and a best approximate value.

Key words: rectangular plate, large deflection, perturbation method, weighted residul method, trail function