Education Journal, Vol. 2, Issue 2, Jun  2019, Pages 29-35; DOI: 10.31058/j.edu.2019.22002 10.31058/j.edu.2019.22002

A Straightforward Program for Formulating General Solid Mechanics Equations in Non Cartesian Geometries for Undergraduate Engineering Students

Education Journal, Vol. 2, Issue 2, Jun  2019, Pages 29-35.

DOI: 10.31058/j.edu.2019.22002

Hector Ariel Di Rado 1 , Pablo Alejandro Beneyto 1*

1 Applied Mechanics Department, Faculty of Engineering, National Northeast University, Resistencia, Argentina

Received: 30 August 2019; Accepted: 20 September 2019; Published: 4 October 2019

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Abstract

Whilst in physics science the use of convected coordinates, non Cartesian geometry or any other geometrical tool is widespread, in undergraduate engineering teaching of continuum mechanics usually a different path is underwent. Even if geometry generalization lie beneath the core of a more closely description of the actual distribution of strain, stress, and displacement, a concise and precise treatment of geometry evolution is frequently overruled in engineering undergraduate courses. The main scope of the present short communication is to provide an explanation to the aforementioned behavior and to put forward different situations in which the main drawbacks induced by the underlain mathematical tools involved in are outbalanced by an all encompassing approach in the development of the main field equation of solid mechanics. Hereinafter, main guidelines for introducing the most relevant equations of solid mechanics in curved space are presented as a natural and easy-to-comprehend extension of Cartesian coordinates. Specifically, a straightforward deduction of differential equilibrium equation in Plane Polar as well as Spherical Polar coordinates is carried out. Whether Euclidean or not, the whole problem boils down to design a simple program carrying out the necessary change of frame, rendering this program a teaching tool that worthwhile to be included in undergraduates courses.

Keywords

Engineering, Education, Geometry, Mathematics, Continuum Mechanics, Non-Euclidean, Convected Coordinates

Copyright

© 2017 by the authors. Licensee International Technology and Science Press Limited. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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