Large Deflection Analysis of a Cantilever Beam with a Certain Angle of Inclination

Abstract Large deflection analysis is crucial for understanding and predicting the mechanical performance of flexible beam structures, which can be used to analyze metamaterial unit cells simplified into flexible beam structures. This paper investigates the large deflection behavior of an inclined cantilever beam with its freedom end subjected to a dead load. Firstly, considering the geometric nonlinearity of the beam and the influence of boundary conditions, a mathematical model of the beam is established and solved. Secondly, equations for the deflection curve and strain energy are derived, expressed in the semi-analytical form of elliptic functions. Then, a program is developed using Riemann integration combined with the bisection method to iteratively obtain the final calculation results. Finally, the calculation results of this paper are compared with those obtained by the nonlinear finite element method, thereby validating the accuracy of the proposed algorithm.