Large Deflection Static Analysis of a Cantilever Beam Subjected to a Point Load

This work presents geometrically non-linear static analysis of a cantilever beam subjected to a non-follower transversal point load at the free end of the beam. The material of the beam is assumed as isotropic and hyperelastic. In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of two dimensional continua for a twelve-node quadratic element. The considered highly nonlinear problem is solved by using incremental displacement-based finite element method in connection with Newton-Raphson iteration method. In the study, the effect of the large deflections and rotations on the displacements and the normal stress and the shear stress distributions through the thickness of the beam is investigated in detail. With the variation of the ratio of Lenght/height, the results of the total Lagrangian finite element model of two dimensional continua for a twelve-node quadratic element are compared with the results of SAP2000 packet program. Also, a few of the obtained results are compared with the previously published results. Numerical results indicate that with decrease the of ratio of lenght/height, using the total Lagrangian finite element model of two dimensional continua plays very important role in the static responses of the beam in geometrically non-linear static analysis.