Structural Engineering and Mechanics

  • 제69권4호
  • /
  • Pages.427-437
  • /
  • 2019
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A refined functional and mixed formulation to static analyses of fgm beams

  • Madenci, Emrah (Department of Civil Engineering, Faculty of Engineering and Architecture, Necmettin Erbakan University)
  • 투고 : 2018.09.11
  • 심사 : 2019.12.29
  • 발행 : 2019.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this study, an alternative solution procedure presented by using variational methods for analysis of shear deformable functionally graded material (FGM) beams with mixed formulation. By using the advantages of $G{\hat{a}}teaux$ differential approaches, a refined complex general functional and boundary conditions which comprises seven independent variables such as displacement, rotation, bending moment and higher-order bending moment, shear force and higher-order shear force, is derived for general thick-thin FGM beams via shear deformation beam theories. The mixed-finite element method (FEM) is employed to obtain a beam element which have a 2-nodes and total fourteen degrees-of-freedoms. A computer program is written to execute the analyses for the present study. The numerical results of analyses obtained for different boundary conditions are presented and compared with results available in the literature.

키워드

참고문헌

  1. Akoz, A. and Kadioglu, F. (1996), "The mixed finite element solution of circular beam on elastic foundation", Comput. Struct., 60(4), 643-651. https://doi.org/10.1016/0045-7949(95)00418-1
  2. Akoz, A. and O zutok, A. (2000), "A functional for shells of arbitrary geometry and a mixed finite element method for parabolic and circular cylindrical shells", Int. J. Numer. Meth. Eng., 47(12), 1933-1981. https://doi.org/10.1002/(SICI)1097-0207(20000430)47:12<1933::AID-NME860>3.0.CO;2-0
  3. Alshorbagy, A.E., Eltaher, M. and Mahmoud, F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Math. Modell., 35(1), 412-425. https://doi.org/10.1016/j.apm.2010.07.006
  4. Aydogdu, M. and Taskin, V. (2007), "Free vibration analysis of functionally graded beams with simply supported edges", Mater. Des., 28(5), 1651-1656. https://doi.org/10.1016/j.matdes.2006.02.007
  5. Bathe, K.J. (2006), Finite Element Procedures, Klaus-Jurgen Bathe.
  6. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Brazil. Soc. Mech. Sci. Eng., 38(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0
  7. Chakraborty, A., Gopalakrishnan, S. and Reddy, J. (2003), "A new beam finite element for the analysis of functionally graded materials", Int. J. Mech. Sci., 45(3), 519-539. https://doi.org/10.1016/S0020-7403(03)00058-4
  8. Eratli, N. and Akoz, A.Y. (2002), "Free vibration analysis of Reissner plates by mixed finite element", Struct. Eng. Mech., 13(3), 277-298. https://doi.org/10.12989/sem.2002.13.3.277
  9. Filippi, M., Carrera, E. and Zenkour, A. (2015), "Static analyses of FGM beams by various theories and finite elements", Compos. Part B: Eng., 72, 1-9. https://doi.org/10.1016/j.compositesb.2014.12.004
  10. Hadji, L., Daouadji, T.H., Meziane, M., Tlidji, Y. and Bedia, E.A.A. (2016), "Analysis of functionally graded beam using a new first-order shear deformation theory", Struct. Eng. Mech., 57(2), 315-325. https://doi.org/10.12989/sem.2016.57.2.315
  11. Hadji, L., Khelifa, Z. and El Abbes, A.B. (2016), "A new higher order shear deformation model for functionally graded beams", KSCE J. Civil Eng., 20(5), 1835-1841. https://doi.org/10.1007/s12205-015-0252-0
  12. Kadoli, R., Akhtar, K. and Ganesan, N. (2008), "Static analysis of functionally graded beams using higher order shear deformation theory", Appl. Math. Modell., 32(12), 2509-2525. https://doi.org/10.1016/j.apm.2007.09.015
  13. Kahya, V. and Turan, M. (2017), "Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory", Compos. Part B: Eng., 109, 108-115. https://doi.org/10.1016/j.compositesb.2016.10.039
  14. Kim, J. and Reddy, J. (2013), "Analytical solutions for bending, vibration, and buckling of FGM plates using a couple stressbased third-order theory", Compos. Struct., 103, 86-98. https://doi.org/10.1016/j.compstruct.2013.03.007
  15. Lee, J.W. and Lee, J.Y. (2017), "Free vibration analysis of functionally graded Bernoulli-Euler beams using an exact transfer matrix expression", Int. J. Mech. Sci., 122, 1-17. https://doi.org/10.1016/j.ijmecsci.2017.01.011
  16. Li, S.R., Cao, D.F. and Wan, Z.Q. (2013), "Bending solutions of FGM Timoshenko beams from those of the homogenous Euler-Bernoulli beams", Appl. Math. Modell., 37(10-11), 7077-7085. https://doi.org/10.1016/j.apm.2013.02.047
  17. Li, X.F. (2008), "A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams", J. Sound Vibr., 318(4-5), 1210-1229. https://doi.org/10.1016/j.jsv.2008.04.056
  18. Li, X.F., Wang, B.L. and Han, J.C. (2010), "A higher-order theory for static and dynamic analyses of functionally graded beams", Arch. Appl. Mech., 80(10), 1197-1212. https://doi.org/10.1007/s00419-010-0435-6
  19. Menaa, R., Tounsi, A., Mouaici, F., Mechab, I., Zidi, M. and Bedia, E.A.A. (2012), "Analytical solutions for static shear correction factor of functionally graded rectangular beams", Mech. Adv. Mater. Struct., 19(8), 641-652. https://doi.org/10.1080/15376494.2011.581409
  20. Mohanty, S., Dash, R. and Rout, T. (2011), "Parametric instability of a functionally graded Timoshenko beam on Winkler's elastic foundation", Nucl. Eng. Des., 241(8), 2698-2715. https://doi.org/10.1016/j.nucengdes.2011.05.040
  21. Murin, J., Aminbaghai, M., Hrabovsky, J., Kutis, V. and Kugler, S. (2013), "Modal analysis of the FGM beams with effect of the shear correction function", Compos. Part B: Eng., 45(1), 1575-1582. https://doi.org/10.1016/j.compositesb.2012.09.084
  22. Nguyen, T.K., Vo, T.P. and Thai, H.T. (2013), "Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory", Compos. Part B: Eng., 55, 147-157. https://doi.org/10.1016/j.compositesb.2013.06.011
  23. Nguyen, T.T., Kim, N.I. and Lee, J. (2016), "Free vibration of thin-walled functionally graded open-section beams", Compos. Part B: Eng., 95, 105-116. https://doi.org/10.1016/j.compositesb.2016.03.057
  24. Oden, J.T. and Reddy, J.N. (1976), "On mixed finite element approximations", SIAM J. Numer. Analy., 13(3), 393-404. https://doi.org/10.1137/0713035
  25. Ozutok, A., Madenci, E. and Kadioglu, F. (2014), "Free vibration analysis of angle-ply laminate composite beams by mixed finite element formulation using the Gateaux differential", Sci. Eng. Compos. Mater., 21(2), 257-266. https://doi.org/10.1515/secm-2013-0043
  26. Ozutok, A. and Madenci, E. (2013), "Free vibration analysis of cross-ply laminated composite beams by mixed finite element formulation", Int. J. Struct. Stab. Dyn., 13(2), 1250056.
  27. Ozutok, A. and Madenci, E. (2017), "Static analysis of laminated composite beams based on higher-order shear deformation theory by using mixed-type finite element method", Int. J. Mech. Sci., 130, 234-243. https://doi.org/10.1016/j.ijmecsci.2017.06.013
  28. Reddy, J. (2000), "Analysis of functionally graded plates", Int. J. Numer. Meth. Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  29. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51(4), 745-752. https://doi.org/10.1115/1.3167719
  30. Reddy, J.N. (2002), Energy Principles and Variational Methods in Applied Mechanics, John Wiley & Sons.
  31. Sankar, B. (2001), "An elasticity solution for functionally graded beams", Compos. Sci. Technol., 61(5), 689-696. https://doi.org/10.1016/S0266-3538(01)00007-0
  32. Shahba, A., Attarnejad, R., Marvi, M.T. and Hajilar, S. (2011), "Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions", Compos. Part B: Eng., 42(4), 801-808. https://doi.org/10.1016/j.compositesb.2011.01.017
  33. Sina, S., Navazi, H. and Haddadpour, H. (2009), "An analytical method for free vibration analysis of functionally graded beams", Mater. Des., 30(3), 741-747. https://doi.org/10.1016/j.matdes.2008.05.015
  34. Thai, H.T. and Vo, T.P. (2012), "Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories", Int. J. Mech. Sci., 62(1), 57-66. https://doi.org/10.1016/j.ijmecsci.2012.05.014
  35. Vo, T.P., Thai, H.T., Nguyen. T.K. and Inam, F. (2014), "Static and vibration analysis of functionally graded beams using refined shear deformation theory", Meccan., 49(1), 155-168. https://doi.org/10.1007/s11012-013-9780-1
  36. Vo, T.P., Thai, H.T., Nguyen, T.K., Inam, F. and Lee, J. (2015), "Static behaviour of functionally graded sandwich beams using a quasi-3D theory", Compos. Part B: Eng., 68, 59-74. https://doi.org/10.1016/j.compositesb.2014.08.030
  37. Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Modell., 30(1), 67-84. https://doi.org/10.1016/j.apm.2005.03.009
  38. Zienkiewicz, O.C., Taylor, R.L., Zienkiewicz, O.C. and Taylor, R.L. (1977), The Finite Element Method, McGraw-Hill, London, U.K.

피인용 문헌

  1. Flow of casson nanofluid along permeable exponentially stretching cylinder: Variation of mass concentration profile vol.38, pp.1, 2019, https://doi.org/10.12989/scs.2021.38.1.033
  2. Analytical calculation method for the axial equivalent elastic modulus of laminated FRP pipes based on three-dimensional stress state vol.77, pp.1, 2021, https://doi.org/10.12989/sem.2021.77.1.137
  3. Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position vol.39, pp.1, 2021, https://doi.org/10.12989/scs.2021.39.1.051
  4. Investigation on the dynamic response of porous FGM beams resting on variable foundation using a new higher order shear deformation theory vol.39, pp.1, 2019, https://doi.org/10.12989/scs.2021.39.1.095
  5. On the free vibration response of laminated composite plates via FEM vol.39, pp.2, 2019, https://doi.org/10.12989/scs.2021.39.2.149
  6. Influence of micromechanical models on the bending response of bidirectional FG beams under linear, uniform, exponential and sinusoidal distributed loading vol.39, pp.2, 2021, https://doi.org/10.12989/scs.2021.39.2.215
  7. Thermoelastic response of functionally graded sandwich plates using a simple integral HSDT vol.91, pp.7, 2019, https://doi.org/10.1007/s00419-021-01973-7
  8. Free vibration analysis of open-cell FG porous beams: analytical, numerical and ANN approaches vol.40, pp.2, 2021, https://doi.org/10.12989/scs.2021.40.2.157
  9. An efficient higher order shear deformation theory for free vibration analysis of functionally graded shells vol.40, pp.2, 2019, https://doi.org/10.12989/scs.2021.40.2.307
  10. The treatment of constraints due to standard boundary conditions in the context of the mixed Web-spline finite element method vol.38, pp.7, 2021, https://doi.org/10.1108/ec-02-2020-0078
  11. Free vibration analysis of carbon nanotube RC nanobeams with variational approaches vol.11, pp.2, 2021, https://doi.org/10.12989/anr.2021.11.2.157
  12. Computer modeling for frequency performance of viscoelastic magneto-electro-elastic annular micro/nanosystem via adaptive tuned deep learning neural network optimization vol.11, pp.2, 2019, https://doi.org/10.12989/anr.2021.11.2.203