Volume 2, Issue 2 (12-2017)                   NMCE 2017, 2(2): 63-76 | Back to browse issues page

XML Print

Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Ghannadiasl A, Mortazavi S. Assessment of bending solution of beam with arbitrary boundary conditions: an accurate comparison of various approaches. NMCE. 2017; 2 (2) :63-76
URL: http://nmce.kntu.ac.ir/article-1-130-en.html
Assistant Professor, Civil Engineering Department, Faculty of Engineering, University of Mohaghegh Ardabili, Iran , aghannadiasl@uma.ac.ir
Abstract:   (757 Views)
Bending responses are the important characteristics of structures. In this paper, the bending solution of the thin and thick beams which are elastically restrained against rotation and translation are presented using various theories. Hence, accurate and direct modeling technique is offered for modeling of the thin and thick beams. The effect of the values of the span-to-depth ratio and type of the beam supports are assessed to state accurate comparison of various theories. Finally, the numerical examples are shown in order to present the evaluation of the efficiency and simplicity of the various theories. The results of the theories are compared with the results of the finite element method (ABAQUS). Based on the results, using the Timoshenko beam theory, the obtained values are in good agreement with the Finite Element modeling for the values of the span-to-depth ratio (L/h) less than 3. On the other hands, due to ignoring the shear deformation effect, the Euler–Bernoulli theory underestimates the deflection of the moderately deep beams (L/h=5).
Full-Text [PDF 937 kb]   (836 Downloads)    
Type of Study: Research | Subject: General

1. [1] Timoshenko, S.P., "On the corrections for shear of the differential equation for transverse vibrations of prismatic bars", Philos. Mag., vol. 41, 1921, p. 744-746. [DOI:10.1080/14786442108636264]
2. [2] Wang, C.M., Reddy, J.N., Lee, K.H., "Shear Deformable Beams and Plates", Amsterdam: Elsevier Science Ltd, 2000, 312 p.
3. [3] Simsek¸ M., Kocaturk, T., "Free vibration analysis of beams by using a third-order shear deformation theory", Sadhana, vol. 32, 2007, p. 167-179. [DOI:10.1007/s12046-007-0015-9]
4. [4] Ghugal, Y.M., Sharma, R., Hyperbolic shear deformation theory for flexure and vibration of thick isotropic beams", Int. J. Comp. Meth., vol. 6, 2009, p. 585-604. [DOI:10.1142/S0219876209002017]
5. [5] Sayyad, A.S., "Comparison of various refined beam theories for the bending and free vibration analysis of thick beams", Appl. Comput. Mech., vol. 5, 2011, p. 217-230.
6. [6] Sayyad, A.S., Ghugal, Y.M., "Flexure of thick beams using new hyperbolic shear deformation theory", Int. J. Mech., vol. 5, 2011, p. 113-122.
7. [7] Naik, U.P., Sayyad, A.S., Shinde, P.N., "Refined beam theory for bending of thick beams subjected to various loading", Elixir Appl. Math., vol. 43, 2012, p. 7004-7015.
8. [8] Labuschagne, A., Van Rensburg, N.J., Van der Merwe, A.J., "Comparison of linear beam theories", Math. Comput. Model., vol. 49, 2009, p. 20-30. [DOI:10.1016/j.mcm.2008.06.006]
9. [9] Yavari, A., Sarkani, S., Moyer, E.T., "On applications of generalized functions to beam bending problems", Int. J. Solids Struct., vol. 37, 2000, p. 5675-5705. [DOI:10.1016/S0020-7683(99)00271-1]
10. [10] Jiang, W., Zhang, G., Chen, L., "Forced response of quadratic nonlinear oscillator: comparison of various approaches", Appl. Math. Mech., vol. 36, 2015, p. 1403-1416. [DOI:10.1007/s10483-015-1991-7]
11. [11] Sayyad, A.S., Ghugal, Y.M., "Single variable refined beam theories for the bending, buckling and free vibration of homogenous beams", Appl. Comput. Mech., vol. 10, 2016, p.
12. [12] Thai, H.T., Vo, T.P., "Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories", Int. J. Mech. Sci., vol. 62, 2012, p. 57-66. [DOI:10.1016/j.ijmecsci.2012.05.014]
13. [13] Mantari, J.L., Oktem, A.S., Soares, C.G., "A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates", Int. J. Solids Struct., vol. 49, 2012, p. 43-53. [DOI:10.1016/j.ijsolstr.2011.09.008]
14. [14] Dan, M., Pagani, A., Carrera, E., "Free vibration analysis of simply supported beams with solid and thin-walled cross-sections using higher-order theories based on displacement variables", Thin-Walled Struct., vol. 98, 2016, p. 478-495. [DOI:10.1016/j.tws.2015.10.012]
15. [15] Petrolo, M., Carrera, E., Alawami, A.S.A.S., "Free vibration analysis of damaged beams via refined models", Advances in Aircraft and Spacecraft Science, vol. 3, 2016, p. 95-112. [DOI:10.12989/aas.2016.3.1.095]
16. [16] Cinefra, M., Carrera, E., Lamberti, A., Petrolo, M., "Best theory diagrams for multilayered plates considering multifield analysis", J. Intel. Mat. Syst. Str., 2017. [DOI:10.1177/1045389X16679018]
17. [17] Choi, I.S., Jang, G.W., Choi, S., Shin, D., Kim, Y.Y., "Higher order analysis of thin-walled beams with axially varying quadrilateral cross sections", Comput. Struct., vol. 179, 2017, p. 127-139. [DOI:10.1016/j.compstruc.2016.10.025]
18. [18] Wang, C.M., "Timoshenko beam-bending solutions in terms of Euler-Bernoulli solutions", J. Eng. Mech., vol. 121, 1995, p. 763-765 [DOI:10.1061/(ASCE)0733-9399(1995)121:6(763)]
19. [19] Janevski, G., Stamenković, M., Seabra, M., "The critical load parameter of a Timoshenko beam with one-step change in cross section, Facta Uni. Series Mech. Eng., vol. 12, 2014, p. 261-276.
20. [20] Carrera, E., Giunta, G., Petrolo, M., "Beam structures: classical and advanced theories", John Wiley and Sons, 2011, 190 p. [DOI:10.1002/9781119978565]
21. [21] Reddy, J.N., "An introduction to the finite element method", McGraw-Hill, 1993.
22. [22] Ghannadiasl, A., Mofid, M., "An analytical solution for free vibration of elastically restrained Timoshenko beam on an arbitrary variable Winkler foundation and under axial load", Latin American Journal of Solids and Structures, vol. 12, 2015, p. 2417-2438. [DOI:10.1590/1679-78251504]
23. [23] ABAQUS, CAE, "Analysis user's manual, Version 6.12. ", 2012.

Add your comments about this article : Your username or Email:

Send email to the article author