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本文用阶梯函数f(x)=sum from i=1 to n-1 ([f(x_i)](x-x_i)_+~0+f(x_0+0),近似地描述了变截面弹性薄板的刚度变化规律,使表述变截面薄板量值关系的变系数偏微分方程,化成常系数偏微分方程;用有限差分方法导出了阶梯截面处的有效刚度,近似地求解了变截面矩形薄板的挠度、内力和屈曲问题。更适用于实际上的阶梯形截面薄板。
In this paper, we use the step function f(x)=sum from i=1 to n-1([f(x_i)](x-x_i)_+~0+f(x_0+0) to describe approximately the variable section elastic thin plate. The law of stiffness change, the variable coefficient partial differential equation expressing the relationship between the variable section thin plate and the value, is transformed into a constant coefficient partial differential equation; the effective stiffness at the step section is derived by the finite difference method, and the deflection of the thin section rectangular plate is approximately solved. , internal forces and buckling problems are more suitable for practical step-shaped sections.