Rigorous versus naïve implementation of the Galerkin method for stepped beams

In this study, we investigate the application of Galerkin’s method to evaluate the deflection of stepped beams. The naïve implementation, as usually executed in the literature, is contrasted with the rigorous version of the Galerkin method. Naïve implementation involves the integration extended over the steps of the beam where the cross-sectional area and flexural rigidity remain constant. Rigorous implementation treats flexural rigidity as the generalized function, with attendant additional terms associated with the derivatives of the generalized function. The above additional terms do not appear in the naïve implementation of the Galerkin method.