两对边自由另两边自由与固定混合支承矩形板的弯曲

摘要

In this paper,the problem for the bending of a thin rectangularplate with two opposite edges free and the other two edges free mixed with built in under hydrostatic pressure is solved through the method of trigonometric series and polynomial expressions.The deflection functions given satisfy the differential equation of thin plate,all the boundary conditions as well as the conditions at free corner points.Consequently ,analytical solutions for this plate are obtained.%本文应用三角级数加多项式的方法解决了两对边自由另两边自由与固定混合支承矩形薄板在静水压力作用下的弯曲问题。给出的挠度函数满足薄板的基本微分方程、全部边界条件以及角点条件。从而得到了这一问题的解析解。