Pure torsion problem in tensor notation
Sławomir Karaś
s.karas@pollub.plDepartment of Roads and Bridges; Faculty of Civil Engineering and Architecture; Lublin University of Technology; (Poland)
https://orcid.org/0000-0002-0626-5582
Abstract
The paper examines the application of the tensor calculus to the classic problem of the pure torsion of prismatic rods. The introduction contains a short description of the reference frames, base vectors, contravariant and covariant vector coordinates when applying the Einstein summation convention. Torsion formulas were derived according to Coulomb’s and Saint-Venant’s theories, while, as a link between the theories, so-called Navier’s error was discussed. Groups of the elasticity theory equations were used.
Keywords:
pure torsion, tensor calculus, covariant/contravariant basses, vector componentsReferences
Green A.E., Zerna W. Theoretical elasticity. Oxford, Clarendon Press, 1968, pp. 457.
Google Scholar
Dullemond K., Peeters K. Introduction to tensor calculus. 1991-2010. www.ita.uni-heidelberg.de /~dullemond/lectures/tensor/tensor.pdf; pp. 53.
Google Scholar
Gurtin M.E., Sternberg E. Linear theory of elasticity, In: Truesdell, C., Ed., Handbuch der Physik, Vol. VIa/2, Springer-Verlag, Berlin, pp. 296.
Google Scholar
Sokolnikoff I.S. Mathematical theory of elasticity. McGraw-Hill, 1956, pp. 476.
Google Scholar
Kaliski S. Pewne problemy brzegowe dynamicznej teorii sprężystości i ciał niesprężystych; (Certain boundary problems of the dynamic theory of elasticity and inelastic bodies). Warszawa, WAT, 1957. pp. 305.
Google Scholar
Kurrer K-E. The history of the theory of structures: from arch analysis to computational mechanics, Ernst & Sohn Verlag, 2008, pp 848; [04.07.2019]. https://doi.org/10.1017/S000192400008756X
Google Scholar
Fung Y.C. Foundation of solid mechanics, Prentice-Hall, 1965, pp. 525.
Google Scholar
Govindaraju L., Sitharam T.G., Applied elasticity for engineers, I K International Publishing House Pvt. Ltd, New Delhi, 2016, pp. 256; https://www.bookdepository.com/Elasticity-for-Engineers-T-G-Sitharam/9789385909344 ; [20.05.2019].
Google Scholar
Mase G.T., Smelser R., Mase G.E., Continuum mechanics for engineers, 3rd Edit., CRC Press, Taylor & Francis Group, 2009, p. 370. https://www.academia.edu/15548859/Continuum_Mechanics_for_Engineers_ Mase_3rd_Edition?auto =download ; [28.05.2019].
Google Scholar
Romano G., Barretta A., Barretta R. On torsion and shear of Saint-Venant beams, European Journal of Mechanics A/Solids 35, 2012, pp. 47-60.
Google Scholar
Raniecki B., Nguyen H.V., Mechanics of isotropic elastic-plastic flow in pressure-sensitive damaging bodies under finite strains, ZAMM, Vol.90, No.9, 2010, pp. 682-700. https://doi.org/10.1002/zamm.200900398
Google Scholar
Authors
Sławomir Karaśs.karas@pollub.pl
Department of Roads and Bridges; Faculty of Civil Engineering and Architecture; Lublin University of Technology; Poland
https://orcid.org/0000-0002-0626-5582
Statistics
Abstract views: 318PDF downloads: 474
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Budownictwo i Architektura supports the open science program. The journal enables Open Access to their publications. Everyone can view, download and forward articles, provided that the terms of the license are respected.
Publishing of articles is possible after submitting a signed statement on the transfer of a license to the Journal.
