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Acta Mechanica

, Volume 230, Issue 11, pp 3861–3873 | Cite as

Rigorous versus naïve implementation of the Galerkin method for stepped beams

  • Isaac ElishakoffEmail author
  • Arvan Prakash Ankitha
  • Alessandro Marzani
Original Paper
  • 70 Downloads

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.

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Notes

Acknowledgements

This work was done when Prakash Ankitha Arvan served as Visiting Scholar at the Florida Atlantic University. She expresses her gratitude to the Department of Civil, Chemical, Environmental, and Materials Engineering, University of Bologna for providing a grant to carry out the thesis at the Florida Atlantic University.

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • Isaac Elishakoff
    • 1
    Email author
  • Arvan Prakash Ankitha
    • 2
  • Alessandro Marzani
    • 2
  1. 1.Department of Ocean and Mechanical EngineeringFlorida Atlantic UniversityBoca RatonUSA
  2. 2.Department of Civil, Chemical, Environmental, and Materials EngineeringUniversity of BolognaBolognaItaly

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