Large and Small Deflection Analysis of a Cantilever Beam

Abstract

This research focuses on the geometrically nonlinear large deflection analysis of a cantilever beam subjected to a concentrated tip load. Initially, a step-by-step development of the theoretical solution is provided and is compared with numerical analysis based on beam and shell elements. It is shown that the large deflections predicted by numerical analysis using beam elements accurately capture the theoretical results as compared to shell elements. Comparison of above deflections with theoretical and numerical approaches based on small deflection theory is also provided to show the extent of latter’s applicability. Finally, it is shown that for a linear elastic working range of common engineering metals, both small and large deflection approaches yield same results and one can adopt the simple small deflection approach for engineering design. It is highlighted that the theoretical approach of large deflection commonly available in design texts is valid only within the linear elastic strain limit and recommends a careful approach to designers. Further, the effect of parametric variation in geometry and stiffness of beam on large deflection, and resulting bending strains and tip reactions are analyzed and discussed.