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计算任意变截面曲梁的位移,是在虚功原理的基础上,对变截面曲梁的面积和惯性矩的倒数,沿其轴线假定呈线性的阶梯状,引用极座标系的单位阶梯函数(θ-θ_i)_+~0的线性组合f(θ)=sum from i=1 to n-1[f(θ_i)](θ-θ_i)_+~0+f(θ_0+0),来描述其几何量的突变现象,用分部积分法导出求任意变截面曲梁位移的公式。若与总和法相比较,在一定的条件下,具有计算量少,精度高的优点,但是应用范围不及总和法广泛。
Calculating the displacement of an arbitrary variable section beam is based on the principle of virtual work. The area of the curved beam and the reciprocal of the moment of inertia are assumed to be linear steps along its axis. The unit step function of the polar coordinate system is cited. The linear combination of (θ-θ_i)_+~0 f(θ)=sum from i=1 to n-1[f(θ_i)](θ-θ_i)_+~0+f(θ_0+0) comes Describe the abrupt change of its geometric quantity, and use the partial integration method to derive the formula for the displacement of curved beam with arbitrary variable section. If compared with the summation method, under certain conditions, it has the advantage of less calculation and high precision, but the application range is not as wide as the summation method.