TORSIONAL SHEAR STRESS IN PRISMATIC BEAMS WITH ARBITRARY CROSS-SECTIONS USING FINITE ELEMENT METHOD
Determining the shear stress of a structural element caused by torsion is a vital problem. The analytical solution of the Saint-Venant torsion is only suitable for simple cross-sections. The numerical method to evaluate the shear stress of complicated cross-sections is indispensable. Many numerical methods have been studied by scientists. Among these studies, Gruttmann proposed an excellent numerical method, which inherited the Saint-Venant theory. However, the use of isoparametric four-noded quadrilateral elements made the method not to reach the best optimization. The objective of this paper is to improve Gruttmann‘s method by using isoparametric eight-noded quadrilateral elements. MATLAB is the language for programming the numerical method. The validated examples have demonstrated that the author’s numerical method is more effective than Gruttmann‘s method.
Timoshenko, S., Goodier, J. N. Theory of Elasticity, by S. Timoshenko and JN Goodier,... McGraw-Hill book Company, 1951.
Ely, J. F., and Zienkiewicz, O.C. "Torsion of compound bars—A relaxation solution." International Journal of Mechanical Sciences 1.4 (1960): 356-365.
Herrmann, L.R. "Elastic torsional analysis of irregular shapes." Journal of the Engineering Mechanics Division 91.6 (1965): 11-19.
Xiao, Q. Z., et al. "An improved hybrid-stress element approach to torsion of shafts." Computers & structures 71.5 (1999): 535-563.
Gruttmann, F., Sauer, R. and Wagner, W. "Shear stresses in prismatic beams with arbitrary cross‐sections." International journal for numerical methods in engineering 45.7 (1999): 865-889.
2021. Available online: http://projects.ce.berkeley.edu/feap/ (accessed on 08 June 2021).
Fialko, S.Y. and Lumelskyy, D.E. "On numerical realization of the problem of torsion and bending of prismatic bars of arbitrary cross section." Journal of Mathematical Sciences 192.6 (2013): 664-681.
Scadsoft. Available online: https://scadsoft.com/en (accessed on 08 June 2021).
Jog, C.S. and Mokashi, I.S. "A finite element method for the Saint-Venant torsion and bending problems for prismatic beams." Computers & Structures 135 (2014): 62-72.
Beheshti, A. "A numerical analysis of Saint-Venant torsion in strain-gradient bars." European Journal of Mechanics-A/Solids 70 (2018): 181-190.
Katsikadelis, J.T. and Sapountzakis, E.J. "Torsion of composite bars by boundary element method." Journal of engineering mechanics 111.9 (1985): 1197-1210.
Gaspari, D. and Aristodemo, M. "Torsion and flexure analysis of orthotropic beams by a boundary element model." Engineering analysis with boundary elements 29.9 (2005): 850-858.
Barone, G., Iacono, F.L. and Navarra, G. "Complex potential by hydrodynamic analogy for the determination of flexure–torsion induced stresses in De Saint Venant beams with boundary singularities." Engineering Analysis with Boundary Elements 37.12 (2013): 1632-1641.
Lee, J.W., Hong, H.K. and Chen, J.T., "Generalized complex variable boundary integral equation for stress fields and torsional rigidity in torsion problems." Engineering Analysis with Boundary Elements 54 (2015): 86-96.
Paradiso, M., et al. "A BEM approach to the evaluation of warping functions in the Saint Venant theory." Engineering Analysis with Boundary Elements 113 (2020): 359-371.
Chen, K. H., et al. "A new error estimation technique for solving torsion bar problem with inclusion by using BEM." Engineering Analysis with Boundary Elements 115 (2020): 168-211.
Chen, J.T. and Lee, Y.T. "Torsional rigidity of a circular bar with multiple circular inclusions using the null-field integral approach." Computational Mechanics 44.2 (2009): 221-232.
Di Paola, M., Pirrotta, A. and Santoro, R. "Line element-less method (LEM) for beam torsion solution (truly no-mesh method)." Acta Mechanica 195.1 (2008): 349-364.
Santoro, R. "The line element-less method analysis of orthotropic beam for the De Saint Venant torsion problem." International journal of mechanical sciences 52.1 (2010): 43-55.
Chen, H., Gomez, J. and Pindera, M.J. "Saint Venant’s torsion of homogeneous and composite bars by the finite volume method." Composite Structures 242 (2020): 112128.
Chen, H., Gomez, J. and Pindera, M.J. "Parametric finite-volume method for Saint Venant’s torsion of arbitrarily shaped cross sections." Composite Structures 256 (2021): 113052.
Allplan Bridge Features. Available online: https://www.allplan.com/products/allplan-bridge-2019-features/ (accessed on 08 June 2021).
Zienkiewicz, O.C., Taylor, R.L. and Zhu, J.Z. The finite element method: its basis and fundamentals. Elsevier, 2005.  Bathe, K.J. "Finite Element Procedures Prentice-Hall." New Jersey 1037 (1996).
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