Heaviside函数的Laplace变换建立超静定梁挠曲线方程

针对不同性质荷载作用下的悬臂梁受力情况，将Heaviside函数直接引入3种悬臂梁的弯矩方程，从而建立了悬臂梁弯矩方程的通用表达式，并对该方程进行Laplace变换，得到了不同荷载作用下的超静定梁挠曲线方程。该方法简化了计算过程，减少了计算量，其结果与结构力学中的已知结论一致。最后列举了一个实例进行分析，证明其是超静定梁挠曲线计算的一种较为快捷的计算方法。

Method of establishing deflection curve of statically indeterminate beam by Laplace transformation of Heaviside function

Heaviside function is introduced to a moment equation of three cantilever beams based on its situations under different loadings to set up a general moment equation of a cantilever beam. And the Laplace transformation is used in this new equation to get a new deflection curve equation of a statically indeterminate beam under different loadings. This method simplifies the calculation process, decreases the computational complexity, and is proved to be in accordance with some known conclusions of structural mechanics. Furthermore, an application example is analyzed, which provides a convenient and fast calculation method to establish deflection curve equation of a statically indeterminate beam in engineering practice.