A new higher order shear and normal deformation theory for functionally graded beams

다국어 초록 (Multilingual Abstract)

In this scientific work, constructing of a novel shear deformation beam model including the stretching effect is of concern for flexural and free vibration responses of functionally graded beams. The particularity of this model is that, in addition to considering the transverse shear deformation and the stretching effect, the zero transverse shear stress condition on the beam surface is assured without introducing the shear correction parameter. By employing the Hamilton's principle together with the concept of the neutral axe's position for such beams, the equations of motion are obtained. Some examples are performed to demonstrate the effects of changing gradients, thickness stretching, and thickness to length ratios on the bending and vibration of functionally graded beams.

참고문헌 (Reference)

1 Tounsi, A., "Vibration and length-dependent flexural rigidity of protein microtubules using higher order shear deformation theory" 266 (266): 250-255, 2010

2 Bachir Bouderba, "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations" 국제구조공학회 14 (14): 85-104, 2013

3 Houari, M. S. A., "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory" 76 : 102-111, 2013

4 Hayat Saidi, "Thermo-mechanical bending response with stretching effect of functionally graded sandwich plates using a novel shear deformation theory" 국제구조공학회 15 (15): 221-245, 2013

5 Fatima Zohra Kettaf, "Thermal buckling of functionally graded sandwich plates using a new hyperbolic shear displacement model" 국제구조공학회 15 (15): 399-423, 2013

6 Morimoto, T., "Thermal buckling of functionally graded rectangular plates subjected to partial heating" 48 (48): 926-937, 2006

7 Tounsi, A., "Thermal buckling behavior of nanobeam using an efficient higher-order nonlocal beam theory" ASCE 3 (3): 37-42, 2013

8 Benzair, A., "The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory" 41 (41): 225404-, 2008

9 Koizumi, M., "The concept of FGM" 34 : 3-10, 1993

10 Talha, M., "Static response and free vibration analysis of FGM plates using higher order shear deformation theory" 34 (34): 3991-4011, 2010

11 Kadoli, R., "Static analysis of functionally graded beams using higher order shear deformation theory" 32 (32): 2509-2525, 2008

12 Gafour, Y., "Sound wave propagation in zigzag double-walled carbon nanotubes embedded in an elastic medium using nonlocal elasticity theory" 48 : 118-123, 2013

13 Heireche, H., "Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity" 40 (40): 2791-2799, 2008

14 Heireche, H., "Sound wave propagation in single – carbon nanotubes with initial axial stress" 104 (104): 014301-, 2008

15 Heireche, H., "Scale effect on wave propagation of double-walled carbon nanotubes with initial axial loading" 19 (19): 185703-, 2008

16 Ke, L. -L., "Postbuckling analysis of edge cracked functionally graded Timoshenko beams under end shortening" 90 (90): 52-160, 2009

17 Amara, K., "Nonlocal elasticity effect on column buckling of multiwalled carbon nanotubes under temperature field" 34 (34): 3933-3942, 2010

18 Tounsi, A., "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes" 1 (1): 1-11, 2013

19 Rabbab Bachir Bouiadjra, "Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory" 국제구조공학회 48 (48): 547-567, 2013

20 Hebali, H., "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates" ASCE 140 (140): 374-383, 2014

21 Benatta, M.A, "Mathematical solution for bending of short hybrid composite beams with variable fibers spacing" 212 (212): 337-348, 2009

22 Suresh, S., "Fundamentals of Functionally Graded Materials"

23 Chakraverty, S., "Free vibration of exponential functionally graded rectangular plates in thermal environment with general boundary conditions" 36 : 132-156, 2014

24 Yang, J., "Free vibration and buckling analyses of functionally graded beams with edge cracks" 83 (83): 48-60, 2008

25 Nedri, K., "Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory" 49 (49): 641-650, 2014

26 Ke, L. -L., "Flexural vibration and elastic buckling of a cracked Timoshenko beam made of functionally graded materials" 16 (16): 488-502, 2009

27 Koizumi, M., "FGM activities in Japan" 28 (28): 1-4, 1997

28 Reddy, J. N., "Energy Principles and Variational Methods in Applied Mechanics" John Wiley & Sons Inc 2002

29 Carrera, E., "Effects of thickness stretching in functionally graded plates and shells" 42 (42): 123-133, 2011

30 Tounsi, A., "Effect of small size on wave propagation in double-walled carbon nanotubes under temperature field" 104 (104): 104301-, 2008

31 Semmah, A., "Effect of chirality on critical buckling temperature of a zigzag single-walled carbon nanotubes using nonlocal continuum theory" 23 (23): 518-522, 2014

32 H.M. Berrabah, "Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams" 국제구조공학회 48 (48): 351-365, 2013

33 Benguediab, S., "Chirality and scale rffects on mechanical buckling properties of zigzag double-walled carbon nanotubes" 57 : 21-24, 2014

34 Neves, A. M. A., "Bending of FGM plates by a sinusoidal plate formulation and collocation with radial basis functions" 38 (38): 368-371, 2011

35 Fouzia Larbi Chaht, "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect" 국제구조공학회 18 (18): 425-442, 2015

36 Zidi, M., "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory" 34 : 24-34, 2014

37 Sankar, B. V., "An elasticity solution for functionally graded beams" 61 (61): 689-696, 2001

38 Ould Larbi, L., "An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams" 41 (41): 421-433, 2013

39 Ait Amar Meziane, M., "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions" 16 (16): 293-318, 2014

40 Belabed, Z., "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates" 60 : 274-283, 2014

41 Li, X. -F., "A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams" 318 (318): 1210-1229, 2008

42 Kada Draiche, "A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass" 국제구조공학회 17 (17): 69-81, 2014

43 Sallai, B. O., "A theoretical analysis of flexional bending of Al/Al2O3 S-FGM thick beams" 44 (44): 1344-1350, 2009

44 Tounsi, A., "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates" 24 (24): 209-220, 2013

45 Neves, A. M. A., "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates" 43 (43): 711-725, 2012

46 Neves, A. M. A., "A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates" 94 (94): 1814-1825, 2012

47 Bousahla, A. A., "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates" 11 (11): 1350082-, 2014

48 Mohamed Bourada, "A new simple shear and normal deformations theory for functionally graded beams" 국제구조공학회 18 (18): 409-423, 2015

49 El Meiche, N., "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate" 53 (53): 237-247, 2011

50 Bessaim, A., "A new higherorder shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets" 15 (15): 671-703, 2013

51 Fekrar, A., "A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates" 49 (49): 795-810, 2014

52 Mohammed Bouremana, "A new first shear deformation beam theory based on neutral surface position for functionally graded beams" 국제구조공학회 15 (15): 467-479, 2013

53 I. Klouche Djedid, "A n-order four variable refined theory for bending and free vibration of functionally graded plates" 국제구조공학회 17 (17): 21-46, 2014

54 Li, X. F., "A higher-order theory for static and dynamic analyses of functionally graded beams" 80 (80): 1197-1212, 2010

55 Benachour, A. ., "A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient" 42 (42): 1386-1394, 2011