Large deflection analysis of cantilever beam under end point and distributed loads

Although the deflection of beams has been studied for decades, the solutions were either linearized (i.e. small deflection) or based on elliptic integrals or functions (large deflection). The latter one includes the geometric nonlinearity but calculation of the deflection along the beam length requires numerical solution of simultaneous equations which is a significant drawback for optimization or reliability analysis. This paper is motivated to overcome these shortcomings by presenting an analytical solution for the large deflection analysis of a cantilever beam under free end point and uniform distributed loads. Direct nonlinear solution by use of homotopy analysis method was implemented to drive the semi-exact solution of trajectory position of any point along the beam length. For the purpose of comparison, the deflections were calculated and compared to those of finite element method which was taken as reference. It was found that the proposed solution is very accurate, efficient, and convenient for the discussed problem and can be applied to a large class of practical problems.