Comparison of Methods for Large Deflection Analysis of a Cantilever Beam Under Free End Point Load Cases

Abstract

The objective of this paper is to present a comparative analysis for large deflections of a cantilever beam under free end point load. pseudo rigid body model (PRBM), non-linear beam theory numerically solved with integration (NLBT-NUM), linear beam theory (LBT), finite element modeling (FEM) using an available commercially FEM package, non-linear beam theory solved with direct nonlinear solution (NLBT-DNS) and experimental evaluation (EXP), have been implemented. For the purpose of comparison, the relation between the displacements, rotating angle of the tip and applied force were calculated and shown graphically. The accuracy of the path of the tip as a function of the force is compared with the NLBT-NUM, which is taken as a reference. In addition, computation times and implementation convenience were recorded. In the case of a perpendicular load, the PRBM is accurate and has little computation time. The NLBT-NUM, NLBT-DNS and FEM analysis are accurate, but the computation time is longer. The NLBT-DNS has been introduced for the first time and provides semi-exact closed form solutions for both horizontal and vertical position. In case of a non-perpendicular load, the NLBT-NUM and FEM analysis are the only accurate methods while computation time is less for the numerical solution. In conclusion, the PRBM and the FEM are recommended for the cases of perpendicular load and non-perpendicular load respectively. Finally, it can be concluded that the more accurate methods take more computation time, and that the accuracy is affected by load cases.