Precise Analysis of the Bending Deformation of the Beam Based on the Chain Rule

Abstract

In order to improve the accuracy of stiffness calculation and derive an accurate rotation angle function and a more accurate deflection function, bu using the chain rule, considering all the higher-order quantities, and combining the relations of higher-order quantities and geometric characteristics, the rotation angle function of the beam was accurately deduced, and the reason for the error of the traditional approximation method was revealed. Consequently a more accurate deflection function was obtained by using the precise rotation angle function. To further verify the reliability of the precise functions, simulation was performed by the method of finite elements. The results show that the value of the angle of rotation obtained by the precise rotation angle function satisfied the finite element simulation results. The accurate rotation angle function was more in line with the actual angle of the beam and was more suitable for practical engineering, which provides a theoretical basis for further approach of the precise deflection function. The calculation result of the accurate rotation angle function can be obtained quickly by related software, which could promote the update of the related software's solution method, and have a wide application prospect.

Keywords

• deflection function
• angle of rotation function
• the chain rule
• the method of finite elements