Fast Processing of Bending Deflection for Euler–Bernoulli Beam Under Different Boundary Constraints Based on a Semi-Analytical Null Space Method

Abstract

In this paper, a semi-analytical method called null space method is proposed to realize fast processing of bending deflection for Euler–Bernoulli beam among various types of boundary constraints. The null space method employs a basis function such as trigonometric function with unknown weight coefficients to approximate the field function. The unknown weight coefficients can be independently solved by the boundary constraint matrix, thus this method can easily keep away from the high demanding of field function to match the given boundary constraint and fastly switch among various types of boundary constraints. The effect of basis function on the final results are first confirmed as compared with the analytical solutions, and the null space method is then applied to predict the settlement of the existing tunnel due to new shield tunneling. The calculated results by null space method gives a good prediction of FEM and in-situ test results.