Flexural-torsional stability of sandwich tapered I-beams with a functionally graded porous core

Document Type : Research

Author

Assistant Professor, Department of civil engineering, University of Kashan, Kashan, Iran.

Abstract

The present research deals with the flexural-torsional buckling analysis of sandwich web and/or flanges tapered doubly-symmetric I-beam. All section walls are composed of two metal face layers and a functionally graded (FG) porous core. It is assumed that the material properties of the porous core vary gradually in the longitudinal direction according to the simple power-law function considering the even distribution of porosities. Based on Vlasov’s theory for thin-walled cross-section, the governing equations are derived via the energy method. The effect of axial load eccentricity is also considered in the formulation. The differential quadrature method is used to estimate the buckling load. In special cases, the results are compared to other available studies. Then the effects of gradient index, axial load eccentricity, porous coefficient, thickness ratio and tapering parameter on stability behavior of a simply supported three-layered sandwich tapered  I-beam with FG porous core are comprehensively assessed. The numerical outcomes of this paper demonstrated that the normalized flexural-torsional buckling load decreases with an increase in the porosity volume fraction.

Keywords


1. Rajasekaran, S. and Nalinaa, K., 2005. Stability and vibration analysis of non-prismatic thin-walled composite spatial members of generic section. International Journal of Structural Stability and Dynamics, 5(04), pp.489-520. [DOI:10.1142/S0219455405001714]
2. Samanta, A. and Kumar, A., 2006. Distortional buckling in monosymmetric I-beams. Thin-walled structures, 44(1), pp.51-56. [DOI:10.1016/j.tws.2005.09.007]
3. Machado, S.P. and Cortínez, V.H., 2007. Free vibration of thin-walled composite beams with static initial stresses and deformations. Engineering Structures, 29(3), pp.372-382. [DOI:10.1016/j.engstruct.2006.05.004]
4. Kurniawan, C.W. and Mahendran, M., 2009. Elastic lateral buckling of simply supported LiteSteel beams subject to transverse loading. Thin-Walled Structures, 47(1), pp.109-119. [DOI:10.1016/j.tws.2008.05.012]
5. Ibanez, J.R. and Serna, M.A., 2010. Equivalent moment approach for elastic lateral-torsional buckling of tapered beams. International Journal of Structural Stability and Dynamics, 10(03), pp.387-409. [DOI:10.1142/S0219455410003543]
6. Yuan, W.B., Kim, B. and Chen, C.Y., 2013. Lateral-torsional buckling of steel web tapered tee-section cantilevers. Journal of Constructional Steel Research, 87, pp.31-37. [DOI:10.1016/j.jcsr.2013.03.026]
7. Li, X.F., Kang, Y.A. and Wu, J.X., 2013. Exact frequency equations of free vibration of exponentially functionally graded beams. Applied Acoustics, 74(3), pp.413-420. [DOI:10.1016/j.apacoust.2012.08.003]
8. Ebrahimi, F. and Mokhtari, M., 2015. Transverse vibration analysis of rotating porous beam with functionally graded microstructure using the differential transform method. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 37(4), pp.1435-1444. [DOI:10.1007/s40430-014-0255-7]
9. Jabbari, M., Mojahedin, A. and Joubaneh, E.F., 2015. Thermal buckling analysis of circular plates made of piezoelectric and saturated porous functionally graded material layers. Journal of Engineering Mechanics, 141(4), p.04014148. [DOI:10.1061/(ASCE)EM.1943-7889.0000872]
10. Chen, D., Yang, J. and Kitipornchai, S., 2016. Free and forced vibrations of shear deformable functionally graded porous beams. International journal of mechanical sciences, 108, pp.14-22. [DOI:10.1016/j.ijmecsci.2016.01.025]
11. Chen, D., Kitipornchai, S. and Yang, J., 2016. Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core. Thin-Walled Structures, 107, pp.39-48. [DOI:10.1016/j.tws.2016.05.025]
12. Saoula, A., Meftah, S.A. and Mohri, F., 2016. Lateral buckling of box beam elements under combined axial and bending loads. Journal of Constructional Steel Research, 116, pp.141-155. [DOI:10.1016/j.jcsr.2015.09.009]
13. Ebrahimi, F. and Jafari, A., 2016. A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities. Journal of Engineering, 2016. [DOI:10.1155/2016/9561504]
14. Shafiei, N. and Kazemi, M., 2017. Buckling analysis on the bi-dimensional functionally graded porous tapered nano-/micro-scale beams. Aerospace Science and Technology, 66, pp.1-11. [DOI:10.1016/j.ast.2017.02.019]
15. Khaniki, H.B. and Rajasekaran, S., 2018. Mechanical analysis of non-uniform bi-directional functionally graded intelligent micro-beams using modified couple stress theory. Materials Research Express, 5(5), p.055703. [DOI:10.1088/2053-1591/aabe62]
16. Lezgy-Nazargah, M., Vidal, P. and Polit, O., 2013. An efficient finite element model for static and dynamic analyses of functionally graded piezoelectric beams. Composite Structures, 104, pp.71-84. [DOI:10.1016/j.compstruct.2013.04.010]
17. Lezgy-Nazargah, M. and Farahbakhsh, M., 2013. Optimum material gradient composition for the functionally graded piezoelectric beams. International Journal of Engineering, Science and Technology, 5(4), pp.80-99. [DOI:10.4314/ijest.v5i4.8]
18. Lezgy-Nazargah, M., 2015. Fully coupled thermo-mechanical analysis of bi-directional FGM beams using NURBS isogeometric finite element approach. Aerospace Science and Technology, 45, pp.154-164. [DOI:10.1016/j.ast.2015.05.006]
19. Lezgy-Nazargah, M., 2017. A generalized layered global-local beam theory for elasto-plastic analysis of thin-walled members. Thin-Walled Structures, 115, pp.48-57. [DOI:10.1016/j.tws.2017.02.004]
20. Lezgy-Nazargah, M. and Meshkani, Z., 2018. An efficient partial mixed finite element model for static and free vibration analyses of FGM plates rested on two-parameter elastic foundations. Struct Eng Mech, 66, pp.665-676.
21. Lezgy-Nazargah M, Vidal P, Polit O. A penalty-based multifiber finite element model for coupled bending and torsional-warping analysis of composite beams. European Journal of Mechanics-A/Solids. 2020; 80:103915. [DOI:10.1016/j.euromechsol.2019.103915]
22. Tang, H., Li, L. and Hu, Y., 2018. Buckling analysis of two-directionally porous beam. Aerospace Science and Technology, 78, pp.471-479. [DOI:10.1016/j.ast.2018.04.045]
23. Nguyen, N.D., Nguyen, T.K., Vo, T.P., Nguyen, T.N. and Lee, S., 2019. Vibration and buckling behaviours of thin-walled composite and functionally graded sandwich I-beams. Composites Part B: Engineering, 166, pp.414-427. [DOI:10.1016/j.compositesb.2019.02.033]
24. Koutoati, K., Mohri, F. and Daya, E.M., 2019. Finite element approach of axial bending coupling on static and vibration behaviors of functionally graded material sandwich beams. Mechanics of Advanced Materials and Structures, pp.1-17. [DOI:10.1080/15376494.2019.1685144]
25. Ghasemi, A.R. and Meskini, M., 2019. Free vibration analysis of porous laminated rotating circular cylindrical shells. Journal of Vibration and Control, 25(18), pp.2494-2508. [DOI:10.1177/1077546319858227]
26. Achref, H., Foudil, M. and Cherif, B., 2019. Higher buckling and lateral buckling strength of unrestrained and braced thin-walled beams: Analytical, numerical and design approach applications. Journal of Constructional Steel Research, 155, pp.1-19. [DOI:10.1016/j.jcsr.2018.12.007]
27. Rajasekaran, S. and Khaniki, H.B., 2019. Bi-directional functionally graded thin-walled non-prismatic Euler beams of generic open/closed cross section Part I: Theoretical formulations. Thin-Walled Structures, 141, pp.627-645. [DOI:10.1016/j.tws.2019.02.006]
28. Asgarian, B., Soltani, M. and Mohri, F., 2013. Lateral-torsional buckling of tapered thin-walled beams with arbitrary cross-sections. Thin-walled structures, 62, pp.96-108. [DOI:10.1016/j.tws.2012.06.007]
29. Soltani, M., Asgarian, B. and Mohri, F., 2014. Elastic instability and free vibration analyses of tapered thin-walled beams by the power series method. Journal of constructional steel research, 96, pp.106-126. [DOI:10.1016/j.jcsr.2013.11.001]
30. Soltani, M., Asil Gharebaghi, S. and Mohri, F., 2018. Lateral stability analysis of steel tapered thin-walled beams under various boundary conditions. Journal of Numerical Methods in Civil Engineering, 3(1), pp.13-25. [DOI:10.29252/nmce.3.1.13]
31. Soltani, M., Asgarian, B. and Mohri, F., 2019. Improved finite element model for lateral stability analysis of axially functionally graded nonprismatic I-beams. International Journal of Structural Stability and Dynamics, 19(09), p.1950108. [DOI:10.1142/S0219455419501086]
32. Soltani, M. and Asgarian, B., 2020. Lateral-Torsional Stability Analysis of a Simply Supported Axially Functionally Graded Beam with a Tapered I-Section. Mechanics of Composite Materials, pp.1-16. [DOI:10.1007/s11029-020-09859-5]
33. Soltani, M. and Asgarian, B., Exact stiffness matrices for lateral-torsional buckling of doubly symmetric tapered beams with axially varying material properties, DOI: 10.1007/s40996-020-00402-z. [DOI:10.1007/s40996-020-00402-z]
34. Yang, Y.Y. and Munz, D., 1997. Stress analysis in a two materials joint with a functionally graded material. In Functionally Graded Materials 1996 (pp. 41-46). Elsevier Science BV. [DOI:10.1016/B978-044482548-3/50008-1]
35. Jin, Z.H. and Paulino, G.H., 2001. Transient thermal stress analysis of an edge crack in a functionally graded material. International Journal of Fracture, 107(1), pp.73-98. [DOI:10.1023/A:1026583903046]
36. Delale, F. and Erdogan, F., 1983. The crack problem for a nonhomogeneous plane. [DOI:10.1115/1.3167098]
37. ZJin, Z.H. and Noda, N., 1994. Crack-tip singular fields in nonhomogeneous materials. [DOI:10.1115/1.2901529]
38. Soltani, M., Asgarian, B. and Mohri, F., 2014. Finite element method for stability and free vibration analyses of non-prismatic thin-walled beams. Thin-Walled Structures, 82, pp.245-261. [DOI:10.1016/j.tws.2014.04.012]