一边支承矩形板弯曲精确解法

一边支承矩形板由于边界条件的多样性导致板中内力分布的复杂性,现有解法存在计算方法不统一,计算精度低,适用范围小等缺陷.提出的精确解法将板的弯曲划分为广义静定和广义超静定两类,对于前者,提出一个统一的通解表达式并采用组合特解,该特解在满足板弯曲平衡徽分方程的同时,还可以满足支承边的挠度条件、自由边上剪力分布条件、自由角点集中力条件及柱支座处的反力条件,从而可以利用四边边界条件及柱支座处的位移条件直接求解.对于广义超静定弯曲,采用叠加法求解.逆向分析算例表明,本解法具有很高的计算精度.

Accurate Solution Method of Rectangular Plate Bending with One Supported Edge

For the rectangular plate bending with a supported edge, the available method has such drawbacks to the different technique as low precision and small suitable region because of the variety of boundary condition. The accurate solution method in this paper divides the plate bending into the generalized statically determinate bending and indeterminate bending, and uses a unified expression of homogeneous solution and composite particular solution for the former. The particular solution can all together satisfy the governing differential equation, the deflection condition along the supported edge, the shear force condition along the free edge, the concentrated force condition at the column support, hence the plate bending can be solved directly by the boundary conditions of four edges and the displacement condition at column support. For the latter the superposition method can be used. The very method has the advantage of high precision and has proved by inverse analysis examples.