Large deformation theory of thin steel cantilever beams under free end load cases

الملخص

In this research, the large deflection of a cantilever tested steel beam of linear elastic material under the action of an external vertical concentrated force at the free end was numerically investigated. The definition of large deflection behavior indicates the inherent nonlinearity found in the response analysis in these beam systems. The analysis pertains to the domain of geometric nonlinearity, often expressing the equilibrium equation in a deformed structure. Numerous authors have implemented various numerical methodologies to address these issues. This paper investigates Rang-kuta numerical techniques for the numerical simulation of the problem. To achieve this purpose, a cantilever beam of length 1 meter and an isotropic thin steel plate with a rectangular cross-section were used. Assuming the beam material is isotropic, with a modulus of elasticity E = 200 GPa and a Poisson's ratio equal zero. The performance of the tested beam was assessed considering deflection and deflection angle. A parametric study is also included to investigate the effect of cross section dimensions (width x height) of steel plate on the bending and the deflection value of tested beams.  The assessments indicate that the proposed method can be widely applied to measure large deflections in thin steel plate materials under concentered loads at the free end of cantilever beams.