Bending response of variable thickness superstatic beams using an Euler model

This paper introduces an application of the Euler beam model to analyze the static bending of thin super static beam structures. The Maple 2017 software (Waterloo Maple Inc., Waterloo, Ontario, Canada) is used to solve the equilibrium equations and boundary condition equations of variable thickness super static beams, which is difficult to do when performing normal calculations that are not supported by calculation software. Two complex computational examples clearly show how the displacement response, rotation angle, and radius of curvature of the beam vary along the length. The results of this study can be applied to analyze complex beam models from macro- to micro-sized beam structures. The Maple code provided in this article may be used and enhanced by students for practical calculation of beam exercises. Moreover, this beam model, together with the Maple beam support, may be used for the analysis of thin beam structures composed of intelligent materials.