In engineering application, beam structure has been widely used, and many scholars have done a lot of research on beam theory for a long time. In essence, beam theory reduces the three-dimensional problem of elasticity theory to one-dimensional problem. Because the thickness is much smaller than the length, it can be approximately considered that the components of displacement, strain and stress are distributed based on the thickness. Due to different approximation methods and different approximation degrees, various beam theories have emerged. Based on the kinematics principle of elastic beam deformation, there are many methods to study beam theory: methods based on various assumptions (including semi-inverse method, trigonometric function method, Fourier series complete expansion method), series expansion method, asymptotic expansion method, gradual approximation method, mixed method and so on. In the series expansion method, Taylor series, McLaughlin series, legendre polynomials and Bernstein polynomials are generally expanded about thickness coordinates. In the asymptotic expansion method, small parameters such as slenderness ratio are usually used. Classical beam theory1At the beginning of the 8th century, based on Euler-Bernoulli hypothesis, the classical beam theory was established. Because the classical beam theory ignores the influence of transverse shear force and transverse normal strain, it is only applicable to long beams. The basic assumption of classical beam theory is that the section perpendicular to the middle plane of the beam before deformation is still plane after deformation and continues to be perpendicular to the middle plane of the beam after deformation. Based on this assumption, the bending deformation of the beam is expressed by the deformation of the beam center line.