三角点或四角点支承的矩形板弯曲统一求解方法

United Solution Method on Rectangular Plate Bending with Three Corner Points Resting or Four Corner Points Resting

提出一种新的挠度表达式 ,可以解决三角点支承的矩形板在任意荷载作用下的弯曲 .该挠度表达式反映板边界条件所能激发出的双向弯曲变形形态 ;所采用的三角级数在相应区间上具有正交性 ,并自然满足支承角点处的位移条件 .分别计算荷载作用下和自由角点单位集中力作用下三角点支承矩形板的弯曲解 ,采用叠加法即可解决四角点支承的矩形板在任意荷载作用下和支承角点发生任意位移时的弯曲 ,后者与理论解答完全相同 .这种解法求解思路清晰 ,收敛速度快 。

In this paper,a new deflection expression is put forward,which can solve the rectangular plate bending with three corner points sustained under arbitrary load.This expression reflects the bending characteristics aroused by the boundary condition and satisfies the displacement condition at the sustained corner points.The triangular series in the expression are orthogonal at the correspondent region.Calculating the plate bending under load and under the unit center force at the free corner points,then the rectangular plate bending with four corner points sustained under arbitrary load or when the sustained points have arbitrary displacement can be soluted using superposition method, and the latter is correspondent to the theorical solution.The method has the advantage of clear thinking,rapidly converging and high precision.