一种计算梁的挠度和转角的新方法

梁的挠曲线方程一般是分段多项式的形式,如果通过某种方法确定了多项式的系数,那么挠曲线方程完全确定。本文利用该思想提出了一种计算梁的挠度和转角的新方法。首先将梁划分为若干区间,然后将每一区间映射到标准区间,在标准区间上以若干点的挠度和转角为待定系数构造梁的挠曲线方程,用配点法得到若干代数方程,最后联合求解所有的代数方程即得到问题的解。新方法计算过程简单,可供教学参考。

A NEW METHOD FOR CALCULATING THE DEFLECTION AND SLOPE ROTATION ANGLE OF A BEAM

The equation of deflection curve of a beam is generally in the form of a piecewise polynomial. If the coefficients of the polynomial are determined by some method, the equation of deflection curve is completely determined. Using this idea, this paper proposes a new method to calculate the deflection and slope rotation angle of a beam. First, the beam is divided into several intervals, and then each interval is mapped to a standard interval, and the equation of deflection curve is constructed with the deflection and slpoe rotation angle of several points as the undetermined coefficients in the standard interval, and the matching point method is used to obtain several algebraic equations, and finally jointly solve the algebraic equations in all intervals to get the solution. The new method simplifies the calculation process and can be used as a teaching reference.