Rigorous versus naïve implementation of the Galerkin method for stepped beams

Authors

• Isaac Elishakoff, Florida Atlantic University
• Arvan Prakash Ankitha, Alma Mater Studiorum Università di Bologna
• Alessandro Marzani, Alma Mater Studiorum Università di Bologna

Author Type

Faculty

Co-Author Type 1

Outside Researcher

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Outside Researcher

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

Acta Mechanica

Publication Status

Version of Record

Abstract

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.

First Page

3861

Last Page

3873

DOI

10.1007/s00707-019-02393-z

Publication Date

11-1-2019

Recommended Citation

Elishakoff, Isaac; Ankitha, Arvan Prakash; and Marzani, Alessandro, "Rigorous versus naïve implementation of the Galerkin method for stepped beams" (2019). Faculty Scholarship. 254.
https://digitalcommons.fau.edu/faculty_papers/254