Pure torsion problem in tensor notation

• Autorzy: Karaś Sławomir

Identyfikatory

DOI

10.24358/Bud-Arch_19_181_06

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

pure torsion; tensor calculus; covariant/contravariant basses; vector components

PL

czysty skręt; rachunek tensorowy; elementy wektorowe

• Wydawca: Wydawnictwo Politechniki Lubelskiej
• Czasopismo: Budownictwo i Architektura
• Rocznik: 2019
• Tom: Vol. 18, nr 1
• Strony: 57--69
• Opis fizyczny: Bibliogr. 10 poz., fig.

Twórcy

autor

Karaś Sławomir

• Department of Roads and Bridges, Faculty of Civil Engineering and Architecture, Lublin University of Technology

Bibliografia

• [1] Green A.E., Zerna W. Theoretical elasticity. Oxford, Clarendon Press, 1968, pp. 457.
• [2] Dullemond K., Peeters K. Introduction to tensor calculus. 1991-2010. www.ita.uni-heidelberg.de /~dullemond/lectures/tensor/tensor.pdf; pp. 53.
• [3] Gurtin M.E., Sternberg E. Linear theory of elasticity, In: Truesdell, C., Ed., Handbuch der Physik, Vol. VIa/2, Springer-Verlag, Berlin, pp. 296.
• [4] Sokolnikoff I.S. Mathematical theory of elasticity. McGraw-Hill, 1956, pp. 476.
• [5] 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.
• [6] Kurrer K-E. The history of the theory of structures: from arch analysis to computational mechanics, Ernst & Sohn Verlag, 2008, DOI: https://doi.org/10.1017/S000192400008756X; pp 848; [04.07.2019] [7] Fung Y.C. Foundation of solid mechanics, Prentice-Hall, 1965, pp. 525.
• [8] 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]. 68 Sławomir Karaś
• [9] 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].
• [10] 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. [11] Raniecki B., Nguyen H.V., Mechanics of isotropic elastic-plastic flow in pressure-sensitive damaging bodies under finite strains, ZAMM, DOI: 10.1002/zamm.200900398, Vol.90, No.9, 2010, pp. 682-700.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).