Application of singular functions in bending deformation of material mechanics

Abstract

In the mechanics of materials, the integral method is often used to calculate the bending deformation of the beam. It is relatively simple to use this method under a single load. However, in real life, the load conditions of most beams are complex and diverse, resulting in more segmentation of the bending equation, too many integral constants, complicated equations involved, cumbersome calculation process, and heavy calculation. In order to solve this problem, the concept of singular function is introduced in this paper. By using a bending equation to express the bending moment internal force of the whole beam, and there are only two integral constants after integration, which greatly simplifies the calculation process and reduces the calculation amount. This paper mainly introduces the properties of the singular function and how to use the singular function to express the bending equation of the beam, and solves the bending deformation of the beam with the boundary conditions, and discusses the application of the singular function in the calculation of the statically indeterminate beam.