Application of singular functions in bending deformation of material mechanics.

This article focuses on the application of singular functions to simplify the calculation of bending deformation in beams within material mechanics. Traditional integral methods require multiple bending moment equations and numerous integral constants when dealing with complex load conditions, leading to cumbersome calculations. By introducing singular functions, the entire beam’s internal forces can be expressed with a single bending moment equation involving only two integral constants, which are determined using boundary conditions, thereby streamlining the computation of rotation angles and deflections. The paper demonstrates this approach for both statically determinate and statically indeterminate beams, showing that singular functions facilitate efficient determination of support reactions, internal forces, and bending deformations even under complex loading scenarios. This method offers a significant reduction in computational complexity and enhances the analysis of mechanical discontinuities in beam structures.