Structural Engineering and Mechanics

  • 제65권6호
  • /
  • Pages.657-678
  • /
  • 2018
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Development of super convergent Euler finite elements for the analysis of sandwich beams with soft core

  • 투고 : 2017.04.27
  • 심사 : 2018.01.10
  • 발행 : 2018.03.25
⟨ 이전 논문 다음 논문 ⟩

초록

Sandwich structures are well known for their use in aircraft, naval and automobile industries due to their high strength resistance with light weight and high energy absorption capability. Sandwich beams with soft core are very common and simple structures that are employed in day to day general use appliances. Modeling and analysis of sandwich structures is not straight forward due to the interactions between core and face sheets. In this paper, formulation of Super Convergent finite elements for analysis of the sandwich beams with soft core based on Euler Bernoulli beam theory are presented. Two elements, Eul4d with 4 degrees of freedom assuming rigid core in transverse direction and Eul10d with 10 degrees of freedom assuming the flexible core were developed are presented. The formulation considers the top, bottom face sheets and core as separate entities and are coupled by beam kinematics. The performance of these elements are validated by results available in the published literature. Number of studies are performed using the formulated elements in static, free vibration and wave propagation analysis involving various boundary and loading conditions. The paper highlights the advantages of the elements developed over the traditional elements for modeling of sandwich beams and, in particular wave propagation analysis.

키워드

참고문헌

  1. Frostig, Y. (2003), "Classical and higher order computational models in the analysis of modern sandwich panels", Compos. Part B: Eng., 34, 83-100.
  2. Frostig, Y. (1992), "Behavior of delaminated sandwich beam with transversely flexible core-high order theory", Compos. Struct., 20, 1-16. https://doi.org/10.1016/0263-8223(92)90007-Y
  3. Frostig, Y. and Baruch, M. (1994), "Free vibrations of sandwich beams with a transversely flexible core: A higher order approach", J. Sound Vibr., 176(2), 195-208. https://doi.org/10.1006/jsvi.1994.1368
  4. Marur, S.R. and Kant, T. (1996), "Free vibration analysis of fiber reinforced composite beams using higher order theories and finite element modeling", J. Sound Vibr., 194(3), 337-351. https://doi.org/10.1006/jsvi.1996.0362
  5. Zhen, W. and Wanji, C. (2008), "An assessment of several displacement-based theories for the vibration and stability analysis of laminated composites and sandwich beams", Compos. Struct., 84(4), 337-349. https://doi.org/10.1016/j.compstruct.2007.10.005
  6. Yang, M. and Qiao, P. (2005), "Higher order impact modelling of sandwich structures with flexible core", J. Sol. Struct., 42, 5460-5490. https://doi.org/10.1016/j.ijsolstr.2005.02.037
  7. Yang, M. and Qiao, P. (2007), "Impact and damage prediction of sandwich beams with flexible core considering arbitrary boundary effects", J. Sandw. Struct. Mater., 9(5), 411-444. https://doi.org/10.1177/1099636207067135
  8. Catherine, N.P., Yeoshua, F. and George, A.K. (2012), "Analysis of sandwich beams with a compliant core and with in-plane rigidity-extended high-order sandwich panel theory versus elasticity", J. Appl. Mech., 79(4).
  9. Li, X.Y. and Liu, D. (1997), "Generalised laminate theories based on double superposition hypothesis", J. Numer. Meth. Eng., 40, 1197-212. https://doi.org/10.1002/(SICI)1097-0207(19970415)40:7<1197::AID-NME109>3.0.CO;2-B
  10. Cho, M. and Parmerter, R. (1993), "Efficient higher order composite plate theory for general lamination configurations", AIAA J., 31, 1299-1306. https://doi.org/10.2514/3.11767
  11. Marco, G. (2013), "On the use of zigzag functions in equivalent single layer theories for laminated composite and sandwich beams: A comparative study and some observations on external weak layers", J. Appl. Mech., 80(6).
  12. Matsunaga, H. (2001), "Vibration and buckling of multi layered composite beams according to higher order deformation theories", J. Sound Vibr., 246, 47-62. https://doi.org/10.1006/jsvi.2000.3627
  13. Kant, T. and Swaminathan, K. (2001), "Analytical solutions for free vibrations of laminated composite and sandwich plates based on a higer order refined theory", Compos. Struct., 53, 73-85.
  14. Reddy, J.N. (1984), "A Simple higher order theory for laminated composite plates", J. Appl. Mech., 51, 745-752. https://doi.org/10.1115/1.3167719
  15. Damanpacka, A.R. and Khalilia, S.M.R. (2012), "High-order free vibration analysis of sandwich beams with a flexible core using dynamic stiffness method", Compos. Struct., 94(5), 1503-1514. https://doi.org/10.1016/j.compstruct.2011.08.023
  16. Ines, I., Carlos, S. and Sonia, S.S. (2010), "FEM analysis of dynamic flexural behaviour of composite sandwich beams with foam core", Compos. Struct., 92(9), 2285-2291. https://doi.org/10.1016/j.compstruct.2009.07.018
  17. Gillich, G.R., Praisach, Z.I., Abdel Wahab, M. and Vasile, O. (2014), "Localization of transversal cracks in sandwich beams and evaluation of their severity", Shock Vibr., 607125, 10.
  18. Wang, Z., Jing, L., Ning, J. and Zhao, L. (2011), "The structural response of clamped sandwich beams subjected to impact loading", Compos. Struct., 93(4), 1300-1308. https://doi.org/10.1016/j.compstruct.2010.05.011
  19. Banerjee, J.R., Cheung, C.W., Morishima, R., Perera, M. and Njuguna, J. (2007), "Free vibration of a three-layered sandwich beam using the dynamic stiffness method and experiment", J. Sol. Struct., 44, 7543-7563. https://doi.org/10.1016/j.ijsolstr.2007.04.024
  20. Tagarielli, V.L., Deshpande, V.S. and Fleck, N.A. (2010), "Prediction of the dynamic response of composite sandwich beams under shock loading", J. Imp. Eng., 37(7), 854-864. https://doi.org/10.1016/j.ijimpeng.2009.11.008
  21. Poortabib, A. and Maghsoudi, M. (2014), "The analytical solution for buckling of curved sandwich beams with a transversely flexible core subjected to uniform load", Struct. Eng. Mech., 52(2).
  22. Mohammadimehr, M. and Shahedi, S. (2016), "Nonlinear magneto-electro-mechanical vibration analysis of double-bonded sandwich Timoshenko microbeams based on MSGT using GDQM", Steel Compos. Struct., 21(1).
  23. Yan, J.B., Liew, J.Y.R. and Zhang, M.H. (2015), "Ultimate strength behavior of steel-concrete-steel sandwich beams with ultra-lightweight cement composite, part 2: Finite element analysis", Steel Compos. Struct., 18(4).
  24. Yusuf, C. (2015), "Free vibration analysis of edge cracked symmetric functionally graded sandwich beams", Struct. Eng. Mech., 56(6).
  25. Noureddine, E.M., Tounsi, A., Ziane, N., Mechab, I. and Adda Bedia, E.A. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", J. Mech. Sci.
  26. Mohamed Ait Amar, M., Hadj, H.A. and Abdelouahed, T. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852
  27. Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2016), "A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates", Steel Compos. Struct., 22(2), 257-276. https://doi.org/10.12989/scs.2016.22.2.257
  28. Boukhari, A., Atmane, H.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., 57(5), 837-859. https://doi.org/10.12989/sem.2016.57.5.837
  29. Hichem, B., Kouider, H.B., Hadji, L., Mohammed, S.A.H. and Abdelouahed, T. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Braz. Soc. Mech. Sci. Eng., 38(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0
  30. Hadj, H.A., Hassen, A.A., Ismail, M., Lakhdar, B., Abelouahed, T., Adda Bedia, E.A. (2011), "Static analysis of functionally graded sandwich plates using an efficient and simple refined theory", Chin. J. Aeronaut., 24(4), 434-448. https://doi.org/10.1016/S1000-9361(11)60051-4
  31. Hadj, H.A., Mohamed, A.A.M., Abdelmoumen, A.B., Abdelouahed, T., Mahmoud, S.R. and Afaf, S.A. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., 25(6), 693-704. https://doi.org/10.12989/SCS.2017.25.6.693
  32. Malekzadeh Fard, K. (2014), "Higher order free vibration of sandwich curved beams with a functionally graded core", Struct. Eng. Mech., 49(5).
  33. Atmane, H.A., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2015), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., 19(2), 369-384. https://doi.org/10.12989/scs.2015.19.2.369
  34. Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  35. Lazreg, H., Zoubida, K. and Adda Bedia, E.A. (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
  36. Habib, H., Abdelouahed, T., Mohammed, S.A.H. and Aicha, B. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", ASCE J. Eng. Mech., 140, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  37. Zakaria, B., Mohammed, S.A.H., Abdelouahed, T., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos.: Part B, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  38. Amale, M.E., Abbas Adda, B. and Abdelouahed, T. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39, 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  39. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  40. Bennai, R., Atmane, H.A. and Tounsi, A. (2015), "A new higherorder shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., 19(3).
  41. Mohamm, M.B., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088
  42. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  43. Abdelouahed, T., Mohammed, S.A.H., Samir, B. and El Abbas, A.B. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  44. Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  45. Ahmed, H., Mohammed, S.A., Houari, S.R.M. and Abdelouahed, T. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  46. Bouderba, B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  47. Abdelmoumen, A.B., Samir, B., Abdelouahed, T. and Mahmoud, S.R. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., 60(2), 313-335. https://doi.org/10.12989/SEM.2016.60.2.313
  48. Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289
  49. Fouzia, E.H., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., 63(5), 585-595. https://doi.org/10.12989/SEM.2017.63.5.585
  50. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., 25(2), 157-175. https://doi.org/10.12989/SCS.2017.25.2.157
  51. Hichem, B., Ahmed, B., Abdelouahed, T., Abdelmoumen, A.B. and Mahmoud, S.R. (2017), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., 25(3), 257-270. https://doi.org/10.12989/SCS.2017.25.3.257
  52. Gopalakrishnan, S. (2000), "A deep rod finite element for structural dynamics and wave propagation problems", J. Numer. Meth. Eng., 48, 731-744. https://doi.org/10.1002/(SICI)1097-0207(20000620)48:5<731::AID-NME901>3.0.CO;2-#
  53. Chakraborty, A., Mahapatra, D.R. and Gopalakrishnan, S. (2002), "Finite element analysis of free vibration and wave propagation in asymmetric composite beams with structural discontinuities", J. Compos. Struct., 55, 23-36. https://doi.org/10.1016/S0263-8223(01)00130-1
  54. Mitra, M., Gopalakrishnan, S. and Seetharam Bhat, M. (2004), "A new super convergent thin walled composite beam for analysis of box beam structures", J. Sol. Struct., 41, 1491-1518 https://doi.org/10.1016/j.ijsolstr.2003.10.024
  55. Murthy, M.V.V.S., Mahapatra, D.R., Badarinarayana, K. and Gopalakrsihnan, S. (2005), "A refined higher order finite element for asymmetric composite beams", Compos. Struct., 67, 27-35. https://doi.org/10.1016/j.compstruct.2004.01.005
  56. Murthy, M.V.V.S., Gopalakrsihnan, S. and Nair, P.S. (2007), "New locking free higher order finite element formulation for composite beams", J. Comput. Mater. Contin., 5(1), 43-62.
  57. Ghosh, D.P. and Goplakrishnan, S. (2007), "A super convergent finite element for composite beams with embedded magnetostrictive patches", Compos. Struct., 79, 315-330. https://doi.org/10.1016/j.compstruct.2006.01.007
  58. Sudhakar, G. and Vijayaraju. (2010), "Development of a new finite element for the analysis of sandwich beams with soft core", J. Sandw. Struct. Mater., 12, 649-683.
  59. Backstrom, D. and Nilson, A.C. (2007), "Modelling the vibration of sandwich beams using frequency-dependent parameters", J. Sound Vibr., 300, 589-611. https://doi.org/10.1016/j.jsv.2006.07.048
  60. Ahmed, K.M. (1971), "Free vibrations of curved sandwich beams by the method of finite elements", J. Sound Vibr., 18(1), 61-74. https://doi.org/10.1016/0022-460X(71)90631-6
  61. Hwu, C. and Chang, W.C. and Gai, H.S. (2004), "Vibration suppression of composite sandwich beams", J. Sound Vibr., 272, 1-20. https://doi.org/10.1016/S0022-460X(03)00302-X
  62. Chen, W.Q., Lv, C.F. and Bian, Z.G. (2003), "Elasticity solution for free vibration of laminated beams", Compos. Struct., 62, 75-82. https://doi.org/10.1016/S0263-8223(03)00086-2
  63. Allen, H.G. (1969), Sandwich Beams, Analysis and Design of Structural Sandwich Panels, 1st Edition, Pergamon Press Ltd, London, U.K.
  64. Gopalakrishnan, S., Chakraborty, A. and Mahapatra, D.R. (2008), Spectral Finite Element Method, Springer-Verlag, New York, U.S.A.
  65. Cook, R.D. and Malkus, D.S. and Plesha, M.E. and Whitt, R.J. (2002), Finite Elements in Structural Dynamics and Vibrations and Plate bending, Concepts and Applications of Finite Element Analysis, 4th Edition, John Wiley and Sons (ASIA) Pte Ltd, Singapore.
  66. Irving, H.S. and Clive, L.D. (2003), Energy an Finite Element Methods in Structural Mechanics, New Age International(P) Limited, Publishers.
  67. Mario, P. (2001), Structural Dynamics Theory and Computation, CBS Publishers and Distributors, New Delhi, India.
  68. Vinson, J.R. (1999), The Behaviour of Sandwich Structures of isotropic and Composite Materials, 1st Edition, Technomic Publishing Company, U.S.A.
  69. Mead, D.J. and Sivakumaran, S. (1961), "The Stodala method applied to sandwich beam vibration", Proceedings of the Symposium on Numerical Methods for Vibration Problems, University of Southampton.