Published January 24, 2013 | Version 15481
Journal article Open

Determination of Extreme Shear Stresses in Teaching Mechanics Using Freely Available Computer Tools

Creators

Description

In the present paper the extreme shear stresses with the corresponding planes are established using the freely available computer tools like the Gnuplot, Sage, R, Python and Octave. In order to support these freely available computer tools, their strong symbolical and graphical abilities are illustrated. The nature of the stationary points obtained by the Method of Lagrangian Multipliers can be determined using freely available computer symbolical tools like Sage. The characters of the stationary points can be explained in the easiest way using freely available computer graphical tools like Gnuplot, Sage, R, Python and Octave. The presented figures improve the understanding of the problem and the obtained solutions for the majority of students of civil or mechanical engineering.

Files

15481.pdf

Files (269.9 kB)

Name Size Download all
md5:b1d8dc1853fd3276b20f987e9e886251
269.9 kB Preview Download

Additional details

References

  • Y. C. Fung, A First Course in Continuum Mechanics. Englewood Cliffs, New Jersey: Prentice-Hall, 1965.
  • G. E. Mase, Continuum Mechanics. New York: McGraw-Hill, 1970.
  • J. Brni'c, Elastomehanika i Plastomehanika (Elasticity and Plasticity). Zagreb: ╦çSkolska knjiga, 1996.
  • Y. C. Fung and P. Tong, Classical and Computational Continuum Mechanics. Singapore: World Scientific Publishing Co. Pte. Ltd., 2001.
  • S. Srp╦çci╦çc, Mehanika Trdnih Teles (Mechanics of Solids). Ljubljana: Univerza v Ljubljani, Fakulteta za gradbeni╦çstvo in geodezijo, 2004.
  • M. Stanek and G. Turk, Osnove Mehanike Trdnih Teles (An Introduction to the Mechanics of Solids). Ljubljana: Univerza v Ljubljani, Fakulteta za gradbeni╦çstvo in geodezijo, 1998.
  • B. ╦ç Stok, Mehanika Deformabilnih Teles, Zbirka Re╦çsenih Problemov, I. in II. del (Continuum Mechanics, Problems with Solutions, I. and II. part). Ljubljana: Univerza v Ljubljani, Fakulteta za strojni╦çstvo, 1988.
  • S. Jensen. (2004) An Introduction to Method of Lagrange Multipliers. (Online). Available: http://www.slimy.com/ steuard/teaching/tutorials/Lagrange.html
  • T. Williams, C. Kelley, R. Lang, D. Kotz, J. Campbell, G. Elber, and A. Woo. (1986) Gnuplot. (Online). Available: http://www.gnuplot.info/ [10] W. Stein. (2005, February) Sage. (Online). Available: http://www.sagemath.org/ [11] R. Ihaka and R. Gentleman. (1993) R. (Online). Available: http://www.rproject. org/ [12] G. van Rossum. (1991) Python. (Online). Available: http://www.python.org/ [13] J. Eaton, W. (1988) Octave. (Online). Available: http://www.gnu.org/software/octave/ [14] L. Wei-Pin, C. Chang-Hsuan, H. Chung-Li, and M. John, "Digital simulation of the transformation of plane stress," Computer Applications in Engineering Education, vol. 17, no. 1, pp. pp. 25-33, 2009. [15] E. Grossmann. (2012) vrml (octave package). (Online). Available: http://octave.sourceforge.net/vrml/overview.html [16] W. Consortium. (1994, November) Vrml. (Online). Available: http://www.web3d.org/x3d/vrml/ [17] M. Kamburelis. view3dscene. (Online). Available: http://castleengine. sourceforge.net/view3dscene.php [18] T. J. Lukka and J. Stewart. (1998) Freewrl. (Online). Available: http://freewrl.sourceforge.net/