任意集中荷载下简支斜板弯曲问题的解析解

Analytic solution on skew plate bending with simply supported under arbitrary concentrated load

利用斜坐标系下斜板的弯曲方程及边界条件,基于级数理论将荷载与挠度作傅立叶无穷级数展开,并对任意位置的集中荷载分解叠加,导出了任意集中荷载作用四边简支斜板弯曲问题的解析解。通过m athem atica语言编程计算,可求得各种斜角、边长比、泊松比情况下的挠度和弯矩。算例将斜板退化为矩形板与已有精确解比较以及将斜板与有限元比较,结果均吻合较好。求解思路清晰,数值收敛性好,结果准确可靠,方法简单实用。

Using the oblique coordinates system parallel to the edge of the plate and a form of infinite Fourier series to represented the deflection and load with decomposition and superposition, the article obtain the deflection and the internal force for a skew plate simply supported under arbitrary concentrated load. It is good anastomotic comparing with the exact solution finite element technique. The idea is distinct,the convergence good,the result accurate and reliable,the metheod brief and practical.