Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Shear correction factors of a new exponential functionally graded porous beams

  • Mohammed Sid Ahmed Houari (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Aicha Bessaim (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Tarek Merzouki (LISV, University of Versailles Saint-Quentin) ;
  • AhmedAmine Daikh (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Aman Garg (State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology) ;
  • Abdelouahed Tounsi (YFL (Yonsei Frontier Lab), Yonsei University) ;
  • Mohamed A. Eltaher (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Mohamed-Ouejdi Belarbi (Laboratoire de Recherche en Genie Civil, LRGC, Universite de Biskra)
  • Received : 2022.12.06
  • Accepted : 2023.08.16
  • Published : 2024.01.10
⟨ Previous Next ⟩

Abstract

This article introduces a novel analytical model for examining the impact of porosity on shear correction factors (SCFs) in functionally graded porous beams (FGPB). The study employs uneven and logarithmic-uneven modified porosity-dependent power-law functions, which are distributed throughout the thickness of the FGP beams. Additionally, a modified exponential-power law function is used to estimate the effective mechanical properties of functionally graded porous beams. The correction factor plays a crucial role in this analysis as it appears as a coefficient in the expression for the transverse shear stress resultant. It compensatesfor the assumption that the shear strain is uniform across the depth of the cross-section. By applying the energy equivalence principle, a general expression for static SCFs in FGPBs is derived. The resulting expression aligns with the findings obtained from Reissner's analysis, particularly when transitioning from the two-dimensional case (plate) to the one-dimensional case (beam). The article presents a convenient algebraic form of the solution and provides new case studies to demonstrate the practicality of the proposed formulation. Numerical results are also presented to illustrate the influence of porosity distribution on SCFs for different types of FGPBs. Furthermore, the article validates the numerical consistency of the mechanical property changesin FG beams without porosity and the SCF by comparing them with available results.

Keywords

References

  1. Abdelrahman, A.A., Esen, I., Ozarpa, C. and Eltaher, M.A. (2021a), "Dynamics of perforated nanobeams subject to moving mass using the nonlocal strain gradient theory", Appl. Math. Model., 96, 215-235. https://doi.org/10.1016/j.apm.2021.03.008. 
  2. Abdelrahman, A.A., Esen, I., Ozarpa, C., Shaltout, R., Eltaher, M.A. and Assie, A.E. (2021), "Dynamics of perforated higher order nanobeams subject to moving load using the nonlocal strain gradient theory", Smart Struct. Syst., 28(4), 515-533. https://doi.org/10.12989/sss.2021.28.4.515. 
  3. Abrate, S. (2006), "Free vibration, buckling, and static deflections of functionally graded plates", Compos. Sci. Technol., 66, 2383- 2394. http://doi.org/10.1016/j.compscitech.2006.02.032. 
  4. Alazwari, M.A., Esen, I., Abdelrahman, A.A., Abdraboh, A.M. and Eltaher, M.A. (2022), "Dynamic analysis of functionally graded (FG) nonlocal strain gradient nanobeams under thermomagnetic fields and moving load", Adv. Nano Res., 12, 231-251. https://doi.org/10.12989/anr.2022.12.3.231. 
  5. Almitani, K.H., Eltaher, M.A., Abdelrahman, A.A. and Abd-ElMottaleb, H.E. (2021), "Finite element based stress and vibration analysis of axially functionally graded rotating beams. Struct. Eng. Mech., 79(1), 23-33. https://doi.org/10.12989/sem.2021.79.1.023. 
  6. Belarbi, M.O., Daikh, A.A., Garg, A., Merzouki, T., Chalak, H.D. and Hirane, H. (2021), "Nonlocal finite element model for the bending and buckling analysis of functionally graded nanobeams using a novel shear deformation theory", Compos. Struct., 264, 113712. https://doi.org/10.1016/j.compstruct.2021.113712. 
  7. Bert, C.W. (1973), "Simplified analysis of static shear factors for beams of nonhomogeneous cross-section", J. Compos. Mater., 7, 525. https://doi.org/10.1177/002199837300700410. 
  8. Bert, C.W. and Gordaninejad, F. (1983), "Transverse shear effects in bimodular composite laminates", J. Compos. Mater., 17, 282. https://doi.org/10.1007/978-3-642-58092-5_11. 
  9. Berthelot, J.M. (1992), Materiaux Composites, Comportement Mecanique et Analyse des Structures, Masson, Paris. 
  10. Bever, M.B. and Duwez, P.F. (1972), "Gradients in composite materials", Mater. Sci. Eng., 10, 1-8. https://doi.org/10.1016/0025-5416(72)90059-6. 
  11. Birman, V. and Bert, C.W. (2002), "On the choice of shear correction factor in sandwich structures", J. Sandw. Struct. Mater., 4, 83. https://doi.org/10.1177/1099636202004001180. 
  12. Chen, D., Yang, J. and Kitipornchai, S. (2015), "Elastic buckling and static bending of shear deformable functionally graded porous beam", Compos. Struct., 133, 54-61. https://doi.org/10.1016/j.compstruct.2015.07.052. 
  13. Daikh, A.A., Belarbi, M.O., Ahmed, D., Houari, M.S.A., Avcar, M., Tounsi, A. and Eltaher, M.A. (2023), "Static analysis of functionally graded plate structures resting on variable elastic foundation under various boundary conditions", Acta Mechanica, 234(2), 775-806. https://doi.org/10.1007/s00707-022-03405-1. 
  14. Daikh, A.A., Drai, A., Houari, M.S.A. and Eltaher, M.A. (2020), "Static analysis of multilayer nonlocal strain gradient nanobeam reinforced by carbon nanotubes", Steel Compos. Struct., 36(6), 643-656. https://doi.org/10.12989/scs.2020.36.6.643. 
  15. Daikh, A.A., Houari, M.S.A., Belarbi, M.O., Chakraverty, S. and Eltaher, M.A. (2022), "Analysis of axially temperaturedependent functionally graded carbon nanotube reinforced composite plates", Eng. Comput., 38(Suppl 3), 2533-2554. https://doi.org/10.1007/s00366-021-01413-8. 
  16. Demirhan, P.A. and Taskin, V. (2019), "Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach", Compos. B Eng., 160, 661-676. http://doi.org/10.1016/j.compositesb.2018.12.020. 
  17. Efraim, E. and Eisenberger, M. (2007), "Exact vibration analysis of variable thickness thick annular isotropic and FGM plates", J. Sound Vib., 299, 720-738. http://doi.org/10.1016/j.jsv.2006.06.068. 
  18. Esen, I. (2013), "A new finite element for transverse vibration of rectangular thin plates under a moving mass", Finite Elem. Anal. Des., 66, 26-35. https://doi.org/10.1016/j.finel.2012.11.005. 
  19. Esen, I. (2015), "A new FEM procedure for transverse and longitudinal vibration analysis of thin rectangular plates subjected to a variable velocity moving load along an arbitrary trajectory", Lat. Am. J. Solid. Struct., 12, 808-830. https://doi.org/10.1590/1679-78251525. 
  20. Esen, I. and Ozmen, R. (2022), "Thermal vibration and buckling of magneto-electro-elastic functionally graded porous nanoplates using nonlocal strain gradient elasticity", Compos. Struct., 296, 115878. https://doi.org/10.1016/j.compstruct.2022.115878. 
  21. Esen, I., Abdelrahman, A.A. and Eltaher, M.A. (2020), "Dynamics analysis of timoshenko perforated microbeams under moving loads", Eng. Comput., 1-17. https://doi.org/10.1007/s00366-020-01212-7. 
  22. Esen, I., Abdelrahman, A.A. and Eltaher, M.A. (2021), "On vibration of sigmoid/symmetric functionally graded nonlocal strain gradient nanobeams under moving load", Int. J. Mech. Mater. Des., 17(3), 721-742. https://doi.org/10.1007/s10999-021-09555-9. 
  23. Esen, I., Alazwari, M.A., Eltaher, M.A. and Abdelrahman, A.A. (2022), "Dynamic response of FG porous nanobeams subjected thermal and magnetic fields under moving load", Steel Compos. Struct., 42(6), 805-826. https://doi.org/10.12989/scs.2022.42.6.805. 
  24. Ferreira, A.J.M., Batra, R.C., Roque, C.M.C., Qian, L.F. and Jorge, R.M.N. (2006), "Natural frequencies of functionally graded plates by a meshless method", Compos. Struct., 75, 593-600. https://doi.org/10.1016/j.compstruct.2006.04.018. 
  25. Goetzel, C.G. and Lavendel, H.W. (1964), "Multiple scale analysis of heterogeneous elastic structures using homogenization theory and Voronoi cell finite element method", Int. J. Solid. Struct., 32, 149-162. https://doi.org/10.1016/0020-7683(94)00097-G. 
  26. Hirane, H., Belarbi, M.O., Houari, M.S.A. and Tounsi, A. (2021), "On the layerwise finite element formulation for static and free vibration analysis of functionally graded sandwich plates", Eng. Comput., 1-29. https://doi.org/10.1007/s00366-020-01250-1. 
  27. Houari, M.S.A., Bessaim, A., Bernard, F., Tounsi, A. and Mahmoud, S.R. (2018), "Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameterr", Steel Compos. Struct., 28(1), 13-24. https://doi.org/10.12989/scs.2018.28.1.013. 
  28. Koc, M.A., Eroglu, M. and Esen, I. (2022), "Dynamic analysis of high-speed train moving on perforated Timoshenko and EulerBernoulli beams", Int. J. Mech. Mater. Des., 18(4), 893-917. https://doi.org/10.1007/s10999-022-09610-z. 
  29. Koizumi, M. (1997), "FGM activities in Japan", Compos Part B, 28, 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9. 
  30. Madabhusi-Raman, P. and Davalos, J.F. (1996), "Static shear correction factor for laminated rectangular beams", Compos. Part B: Eng., 27, 285-293. https://doi.org/10.1016/1359-8368(95)00014-3. 
  31. Menaa, R., Tounsi, A., Mouaici, F., Mechab, I., Zidi, M. and Bedia, A. (2012), "Analytical solutions for static shear correction factor of functionally graded rectangular beams", Mech. Adv. Mater. Struct., 19, 641-652. https://doi.org/10.1080/15376494.2011.581409. 
  32. Merdaci, S., Mostefa, A.H., Beldjelili, Y., Merazi, M., Boutaleb, S. and Hellal, H. (2019), "Free vibration analysis of functionally", Int. J. Eng. Tech. Res., 8(03), https://doi.org/10.17577/IJERTV8IS030098. 
  33. Merzouki, T., Ahmed, H.M.S., Bessaim, A., Haboussi, M., Dimitri, R. and Tornabene, F. (2022b), "Bending analysis of functionally graded porous nanocomposite beams based on a non-local strain gradient theory", Math. Mech. Solid., 27(1), 66-92. https://doi.org/10.1177/10812865211011759. 
  34. Merzouki, T., Houari, M.S.A., Haboussi, M., Bessaim, A. and Ganapathi, M. (2022a), "Nonlocal strain gradient finite element analysis of nanobeams using two-variable trigonometric shear deformation theory", Eng. Comput., 38(Suppl 1), 647-665. https://doi.org/10.1007/s00366-020-01156-y. 
  35. Mouaici, F., Benyoucef, S., Ait Atmane, H. and Tounsi, A. (2016), "Effect of porosity on vibrational characteristics of nonhomogeneous plates using hyperbolic shear deformation theory", Wind Struct., 22(4), 429-454. https://doi.org/10.12989/was.2016.22.4.429. 
  36. Ngoc, N.M., Hoang, V.N. and Lee, D. (2022), "Concurrent topology optimization of coated structure for non-homogeneous materials under buckling criteria", Eng. Comput., 38(6), 5635-5656. https://doi.org/10.1007/s00366-022-01718-2. 
  37. Nguyen, M.N., Hoang, V.N. and Lee, D. (2023c), "Multiscale topology optimization with stress, buckling and dynamic constraints using adaptive geometric components", Thin Wall. Struct., 183, 110405. https://doi.org/10.1016/j.tws.2022.110405. 
  38. Nguyen, M.N., Jung, W.S., Shin, S.M., Kang, J.W. and Lee, D.K. (2023a), "Topology optimization of Reissner-Mindlin plates using multi-material discrete shear gap method", Steel Compos. Struct., 47(3), 365-374. https://doi.org/10.12989/scs.2023.47.3.365. 
  39. Nguyen, M.N., Lee, D.K., Kang, J.W. and Shin, S.M. (2023b), "Topology optimization with functionally graded multi-material for elastic buckling criteria", Steel Compos. Struct., 46(1), 33-51. https://doi.org/10.12989/scs.2023.46.1.033. 
  40. Nguyen, T.K., Sab, K. and Bonnet, G. (2006), "A ReissnerMindlin model for functionally graded materials", 3rd European Conference on Computational Mechanics, Lisbon, Portugal. 
  41. Nguyen, T.K., Sab, K. and Bonnet, G. (2008), "First-order shear deformation plate models for functionally graded materials", Compos. Struct., 83, 25-36. https://doi.org/10.1016/j.compstruct.2007.03.004. 
  42. Noor, A.K. and Burton, W.S. (1989), "Assessment of shear deformation theories for multilayered composite plates", Appl. Mech. Rev., 42, 1-13. https://doi.org/10.1115/1.3152418. 
  43. Noor, A.K. and Burton, W.S. (1989), "Stress and free vibration analyses of multilayered composite plates", Compos. Struct., 11, 183-204. https://doi.org/10.1016/0263-8223(89)90058-5. 
  44. Noor, A.K. and Burton, W.S. (1990), "Assessment of computational models for multilayered anisotropic plates", Compos. Struct., 14, 233-265. https://doi.org/10.1016/0263-8223(90)90050-O. 
  45. Noor, A.K., Burton, W.S. and Peters, J.M. (1990), "Predictorcorrector procedure for stress and free vibration analyses of multilayered composite plates and shells", Comput. Mech. Appl. Mech. Eng., 82, 341-364. https://doi.org/10.1016/0045-7825(90)90171-H. 
  46. Ozmen, R., Kilic, R. and Esen, I. (2022), "Thermomechanical vibration and buckling response of nonlocal strain gradient porous FG nanobeams subjected to magnetic and thermal fields", Mech. Adv. Mater. Struct., 1-20. https://doi.org/10.1080/15376494.2022.2124000. 
  47. Reddy, J.N. (2002), Energy Principles and Variational Methods in Applied Mechanics, Wiley, New York. 
  48. Rezaei, A.S. and Saidi, A.R. (2015), "Exact solution for free vibration of thick rectangular plates made of porous materials", Compos. Struct., 134, 1051-1060. https://doi.org/10.1016/j.compstruct.2015.08.125. 
  49. Rezaei, A.S. and Saidi, A.R. (2016), "Application of Carrera Unified Formulation to study the effect of porosity on natural frequencies of thick porous-cellular plates", Compos. B Eng., 91, 361-370. https://doi.org/10.1016/j.compositesb.2015.12.050. 
  50. Rezaei, A.S. and Saidi, A.R. (2017), "Buckling response of moderately thick fluid-infiltrated porous annular sector plates", Acta Mech., 228, 3929-3945. https://doi.org/10.1007/s00707-017-1908-2. 
  51. Rezaei, A.S. and Saidi, A.R. (2017), "On the effect of coupled solid-fluid deformation on natural frequencies of fluid saturated porousplates", Eur. J. Mech. Solid., 63, 99-109. https://doi.org/10.1016/j.euromechsol.2016.12.006. 
  52. Sadoun, M., Houari, M.S.A., Bakora, A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2018), "Vibration analysis of thinck orthotropic plates using quasi 3D sinusoidal shear deformation theory", Geomech. Eng., 16(2), 141-150. https://doi.org/10.12989/gae.2018.16.2.141. 
  53. Sadoune, M., Tounsi, A. and Houari, M.S.A. (2014), "A novel first-order shear deformation theory for laminated composite plates", Steel Compos. Struct., 17(3), 321-331. https://doi.org/10.12989/scs.2014.17.3.1321. 
  54. Saidi, H. and Sahla, M. (2019), "Vibration analysis of functionally graded plates with porosity composed of a mixture of Aluminum (Al) and Alumina (Al2O3) embedded in an elastic medium", Frattura ed Integrita Strutturale, 50, 286-299. https://doi.org/10.3221/IGF-ESIS.50.24. 
  55. Selmi, A. (2021), "Vibration behavior of bi-dimensional functionally graded beams", Struct. Eng. Mech., 77(5), 587-599. https://doi.org/10.12989/sem.2021.77.5.587. 
  56. Shahsavari, D., Karami, B., Fahham, H.R. and Li, L. (2018), "On the shear buckling of porous nanoplates using a new sizedependent quasi-3D shear deformation theory", Acta Mech., 229(11), 4549-4573. https://doi.org/10.1007/s00707-018-2247-7. 
  57. Singh, S.J. and Harsha, S.P. (2020b), "Thermo-mechanical analysis of porous sandwich S-FGM plate for different boundary conditions using Galerkin Vlasov's method, a semi analytical approach", Thin Wall. Struct., 150, 106668. https://doi.org/10.1016/j. tws.2020.106668. 
  58. Soltani, K., Bessaim, A., Houari, M.S.A., Kaci, A., Benguediab, M., Tounsi, A. and Alhodaly, M.S. (2019), "A novel hyperbolic shear deformation theory for the mechanical buckling analysis of advanced composite plates resting on elastic foundations", Steel Compos. Struct., 30(1), 13-29. https://doi.org/10.12989/scs.2019.30.1.013. 
  59. Sursh, S. and Mortensen, A. (1998), Fundamentals of Functionally Graded Material: Processing and Thermomecanical Behaviour of Graded Metal and Metal-Ceramic Composites, Press, Cambridge. 
  60. Timoshenko, S.P. (1922), "On the transverse vibrations of bars of uniform cross section", Philos. Mag., 43, 125-131. https://doi.org/10.1080/14786442208633855. 
  61. Tran, T.T., Tran, V.K., Pham, Q.H. and Zenkour, A.M. (2021), "Extended four-unknown higher-order shear deformation nonlocal theory for bending, buckling and free vibration of functionally graded porous nanoshell resting on elastic foundation", Compos. Struct., 264, 113737. https://doi.org/10.1016/j.compstruct.113737. 
  62. Vlachoutsis, S. (1992), "Shear correction factors for plates and shells", Int. J. Numer. Meth. Eng., 33, 1537-1552. https://doi.org/10.1002/nme.1620330712. 
  63. Wang, Y.Q. and Zu, J.W. (2017), "Large-amplitude vibration of sigmoid functionally graded thin plates with porosities", Thin Wall. Struct., 119, 911-924. https://doi.org/10.1016/j.tws.08.012. 
  64. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002. 
  65. Whitney, J.M. (1973), "Shear correction factors for orthotropic laminates under static load", J. Appl. Mech., 40, 302. 
  66. Whitney, J.M., Browning, C.E. and Mair, A. (1974), "Analysis of the flexure test for laminated composite materials", Compos. Mater., Test. Des., 546, 30-45.  https://doi.org/10.1520/STP35481S
  67. Zenkour, A.M. (2018), "A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities", Compos. Struct., 201, 38-48. https://doi.org/10.1016/j.compstruct.05.147. 
  68. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Free vibration analysis of functionally graded plates using the element-free kpRitz method", J. Sound Vib., 319, 918-939. https://doi.org/10.1016/j.jsv.2008.06.025.