用DQ法分析变厚度圆形板的轴对称弯曲

Axisymmetrical Bending of Tapered Circular Plates by Differential Quadrature Method

变厚度圆板在生产工程中得到大量应用,但是相应的分析工作则相对较少。原因之一是由于板的厚度随径向坐标而变化,使得控制微分方程是变系数的。一般情况下,很难求得解析形式的解。文章采用DQ法离散该变系数微分方程,从而求得数值解。最后的算例表明该方法精度较高且简便易行,特别适于工程技术人员在微机上应用。

Tapered thickness circular plates are widely used recently. Due to their variable thickness, the governing differential equation has variable coefficients and cannot be solved analytically in most situations. In this paper, by employing the differential quadrature method, the governing equation is rendered in a discrete form, i.e., a linear equation set. The numerical results are then obtained and compared with those available in literatures. The results show that the presented method can be used easily in personal computers with good precise.