Static analysis of sandwich plates embedded with shape memory alloy wires using active strain energy tuning method

  • Bahareh Akhavan-Rad
  • Mohammad Mahdi KheirikhahEmail author
Technical Paper


In this study, static analysis of sandwich plates with flexible core and composite face sheets embedded with shape memory alloy (SMA) wires in the face sheets is conducted. Third-order plate theory is used to model face sheets, and quadratic and cubic functions are assumed for transverse and in-plane displacements of the flexible core. Continuity conditions of transverse shear stresses at the interfaces between face sheets and core and the zero transverse shear stresses conditions on the upper and lower face sheets are satisfied. Also, transverse flexibility and transverse normal strain and stress of the orthotropic core are noted. The SMA wires are placed in the laminated composite face sheets. Constitutive equation of the SMA wires is employed for modeling their behavior. Nonlinear equations of motion and boundary conditions of sandwich plates are derived using Hamilton’s principle. The nonlinear governing equations of the simply supported sandwich plates under uniform and sinusoidal transverse loads are solved based on Navier’s method. The effect of activating embedded SMA wires on bending behavior of composite sandwich plates are investigated using the active strain energy tuning method. The Liang’s constitutive model is employed to obtain the SMA wires recovery force. The obtained results show that activating SMA wires causes a decrease in the deflection and stresses in these plates.


Shape memory alloy Analytical solution Composite Sandwich plates Bending analysis 



  1. 1.
    Choi S, Lee JJ, Seo DC, Choi SW (1999) The active buckling control of laminated composite beams with embedded shape memory alloy wires. Compos Struct 1(47):679–686Google Scholar
  2. 2.
    Sun G, Sun S, Wu X, Wu J (2000) A study on thermomechanical deformation of elastic beam with embedded shape memory alloy wires. Mater Des 21(6):525–528Google Scholar
  3. 3.
    Lau KT (2002) Vibration characteristics of SMA composite beams with different boundary conditions. Mater Des 23(8):741–749Google Scholar
  4. 4.
    Ghomshei MM, Tabandeh N, Ghazavi A, Gordaninejad F (2005) Nonlinear transient response of a thick composite beam with shape memory alloy layers. Compos B Eng 36(1):9–24Google Scholar
  5. 5.
    Zhang Y, Zhao YP (2007) A study of composite beam with shape memory alloy arbitrarily embedded under thermal and mechanical loadings. Mater Des 28(4):1096–1115Google Scholar
  6. 6.
    Lu P, Cui FS, Tan MJ (2009) A theoretical model for the bending of a laminated beam with SMA fiber embedded layer. Compos Struct 90(4):458–464Google Scholar
  7. 7.
    Zhou G, Lloyd P (2009) Design, manufacture and evaluation of bending behaviour of composite beams embedded with SMA wires. Compos Sci Technol 69(13):2034–2041Google Scholar
  8. 8.
    Khalili SM, Dehkordi MB, Shariyat M (2013) Modeling and transient dynamic analysis of pseudoelastic SMA hybrid composite beam. Appl Math Comput 219(18):9762–9782MathSciNetzbMATHGoogle Scholar
  9. 9.
    Asadi H, Bodaghi M, Shakeri M, Aghdam MM (2013) On the free vibration of thermally pre/post-buckled shear deformable SMA hybrid composite beams. Aerosp Sci Technol 31(1):73–86Google Scholar
  10. 10.
    Yuvaraja M, Senthilkumar M (2013) Comparative study on vibration characteristics of a flexible GFRP composite beam using SMA and PZT actuators. Procedia Eng 64:571–581Google Scholar
  11. 11.
    Damanpack AR, Bodaghi M, Aghdam MM, Shakeri M (2014) Shape control of shape memory alloy composite beams in the post-buckling regime. Aerosp Sci Technol 39:575–587Google Scholar
  12. 12.
    Damanpack AR, Bodaghi M, Aghdam MM, Shakeri M (2014) On the vibration control capability of shape memory alloy composite beams. Compos Struct 110:325–334Google Scholar
  13. 13.
    Alebrahim R, Haris SM, Mohamed NA, Abdullah S (2015) Vibration analysis of self-healing hybrid composite beam under moving mass. Compos Struct 119:463–476Google Scholar
  14. 14.
    Samadpour M, Asadi H, Wang Q (2016) Nonlinear aero-thermal flutter postponement of supersonic laminated composite beams with shape memory alloys. Eur J Mech-A/Solids 57:18–28MathSciNetzbMATHGoogle Scholar
  15. 15.
    Birman V, Chandrashekhara K, Sain S (1996) An approach to optimization of shape memory alloy hybrid composite plates subjected to low-velocity impact. Compos B Eng 27(5):439–446Google Scholar
  16. 16.
    Lee HJ, Lee JJ, Huh JS (1999) A simulation study on the thermal buckling behavior of laminated composite shells with embedded shape memory alloy (SMA) wires. Compos Struct 47(1–4):463–469Google Scholar
  17. 17.
    Thompson SP, Loughlan J (2000) The control of the post-buckling response in thin composite plates using smart technology. Thin-Walled Struct 36(4):231–263Google Scholar
  18. 18.
    Lu ZK, Weng GJ (2000) A two-level micromechanical theory for a shape-memory alloy reinforced composite. Int J Plast 16(10–11):1289–1307zbMATHGoogle Scholar
  19. 19.
    Ostachowicz WM, Kaczmarczyk S (2001) Vibrations of composite plates with SMA fibres in a gas stream with defects of the type of delamination. Compos Struct 54(2–3):305–311Google Scholar
  20. 20.
    Żak AJ, Cartmell MP, Ostachowicz WM (2003) A sensitivity analysis of the dynamic performance of a composite plate with shape memory alloy wires. Compos Struct 60(2):145–157Google Scholar
  21. 21.
    Park JS, Kim JH, Moon SH (2004) Vibration of thermally post-buckled composite plates embedded with shape memory alloy fibers. Compos Struct 63(2):179–188Google Scholar
  22. 22.
    Park JS, Kim JH, Moon SH (2005) Thermal post-buckling and flutter characteristics of composite plates embedded with shape memory alloy fibers. Compos B Eng 36(8):627–636Google Scholar
  23. 23.
    Meo M, Antonucci E, Duclaux P, Giordano M (2005) Finite element simulation of low velocity impact on shape memory alloy composite plates. Compos Struct 71(3–4):337–342Google Scholar
  24. 24.
    Zhang RX, Ni QQ, Masuda A, Yamamura T, Iwamoto M (2006) Vibration characteristics of laminated composite plates with embedded shape memory alloys. Compos Struct 74(4):389–398Google Scholar
  25. 25.
    Khalili SM, Shokuhfar A, Ghasemi FA (2007) Effect of smart stiffening procedure on low-velocity impact response of smart structures. J Mater Process Technol 190(1–3):142–152Google Scholar
  26. 26.
    Khalili SM, Shokuhfar A, Malekzadeh K, Ghasemi FA (2007) Low-velocity impact response of active thin-walled hybrid composite structures embedded with SMA wires. Thin-Walled Struct 45(9):799–808Google Scholar
  27. 27.
    Yongsheng R, Shuangshuang S (2007) Large amplitude flexural vibration of the orthotropic composite plate embedded with shape memory alloy fibers. Chin J Aeronaut 20(5):415–424Google Scholar
  28. 28.
    John S, Hariri M (2008) Effect of shape memory alloy actuation on the dynamic response of polymeric composite plates. Compos A Appl Sci Manuf 39(5):769–776Google Scholar
  29. 29.
    Kuo SY, Shiau LC, Chen KH (2009) Buckling analysis of shape memory alloy reinforced composite laminates. Compos Struct 90(2):188–195Google Scholar
  30. 30.
    Taheri-Behrooz F, Taheri F, Hosseinzadeh R (2011) Characterization of a shape memory alloy hybrid composite plate subject to static loading. Mater Des 32(5):2923–2933Google Scholar
  31. 31.
    Kuang KS, Quek ST, Cantwell WJ (2013) Active control of a smart composite with shape memory alloy sheet using a plastic optical fiber sensor. Sens Actuators A 201:182–187Google Scholar
  32. 32.
    Panda SK, Singh BN (2013) Nonlinear finite element analysis of thermal post-buckling vibration of laminated composite shell panel embedded with SMA fibre. Aerosp Sci Technol 29(1):47–57Google Scholar
  33. 33.
    Shariyat M, Moradi M, Samaee S (2014) Enhanced model for nonlinear dynamic analysis of rectangular composite plates with embedded SMA wires, considering the instantaneous local phase changes. Compos Struct 109:106–118Google Scholar
  34. 34.
    Roh JH, Kim JS, Kwon OH (2015) Vibration behaviors of hybrid smart composites with SMA strips reinforced SMP lamina under blast loading. Compos Struct 125:417–424Google Scholar
  35. 35.
    Bodaghi M, Shakeri M, Aghdam MM (2015) Thermo-mechanical behavior of shape adaptive composite plates with surface-bonded shape memory alloy ribbons. Compos Struct 119:115–133Google Scholar
  36. 36.
    Shariyat M, Niknami A (2016) Impact analysis of strain-rate-dependent composite plates with SMA wires in thermal environments: proposing refined coupled thermoelasticity, constitutive, and contact models. Compos Struct 136:191–203Google Scholar
  37. 37.
    Kheirikhah MM, Khadem M, Farahpour P (2012) Bending analysis of soft core sandwich plates with embedded shape memory alloy wires using three-dimensional finite element method. Proc Inst Mech Eng L J Mater Des Appl 226(3):186–202Google Scholar
  38. 38.
    Khalili SM, Dehkordi MB, Carrera E, Shariyat M (2013) Non-linear dynamic analysis of a sandwich beam with pseudoelastic SMA hybrid composite faces based on higher order finite element theory. Compos Struct 96:243–255Google Scholar
  39. 39.
    Khanjani M, Shakeri M, Sedighi M (2015) Non-linear transient and damping analysis of a long cylindrical sandwich panel with embedded SMA wires. Aerosp Sci Technol 47:98–113Google Scholar
  40. 40.
    Samadpour M, Sadighi M, Shakeri M, Zamani HA (2015) Vibration analysis of thermally buckled SMA hybrid composite sandwich plate. Compos Struct 119:251–263Google Scholar
  41. 41.
    Dehkordi MB, Khalili SM, Carrera E (2016) Non-linear transient dynamic analysis of sandwich plate with composite face-sheets embedded with shape memory alloy wires and flexible core-based on the mixed LW (layer-wise)/ESL (equivalent single layer) models. Compos B Eng 15:59–74Google Scholar
  42. 42.
    Ghaznavi A, Shariyat M (2017) Non-linear layerwise dynamic response analysis of sandwich plates with soft auxetic cores and embedded SMA wires experiencing cyclic loadings. Compos Struct 171:185–197Google Scholar
  43. 43.
    Kheirikhah MM, Khosravi P (2018) Buckling and free vibration analyses of composite sandwich plates reinforced by shape-memory alloy wires. J Braz Soc Mech Sci Eng 40:515Google Scholar
  44. 44.
    Kheirikhah MM, Khalili SM, Fard KM (2012) Biaxial buckling analysis of soft-core composite sandwich plates using improved high-order theory. Eur J Mech A/Solids 31(1):54–66MathSciNetzbMATHGoogle Scholar
  45. 45.
    Kheirikhah MM, Khalili SM, Malekzadeh Fard K (2012) Analytical solution for bending analysis of soft-core composite sandwich plates using improved high-order theory. Struct Eng Mech 44(1):15–34zbMATHGoogle Scholar
  46. 46.
    Khalili SM, Kheirikhah MM, Fard KM (2014) Biaxial wrinkling analysis of composite-faced sandwich plates with soft core using improved high-order theory. Eur J Mech A/Solids 43:68–77MathSciNetzbMATHGoogle Scholar
  47. 47.
    Kheirikhah MM, Khalili MR (2012) Wrinkling analysis of rectangular soft-core composite sandwich plates. In: Öchsner A, da Silva L, Altenbach H (eds) Mechanics and properties of composed materials and structures. Springer, Berlin, pp 35–59Google Scholar
  48. 48.
    Ganilova OA, Cartmell MP (2010) An analytical model for the vibration of a composite plate containing an embedded periodic shape memory alloy structure. Compos Struct 92:39–47Google Scholar
  49. 49.
    Liang C, Rogers CA (1992) Design of shape memory alloy actuators for robotics. In: 4th ASME international symposium on robotics and manufacturing, pp 75–80Google Scholar
  50. 50.
    Kheirikhah MM, Khodayari A, Tatlari M (2013) Design and construction of an artificial finger based on SMA Actuators. Indian J Sci Technol 6(1):3841–3848Google Scholar
  51. 51.
    Kheirikhah MM, Babaghasabha V (2016) Bending and buckling analysis of corrugated composite sandwich plates. J Braz Soc Mech Sci Eng 38:2571–2588Google Scholar
  52. 52.
    Pagano NJ (1970) Exact solutions for rectangular bidirectional composites and sandwich plates. J Compos Mater 4(1):20–34Google Scholar
  53. 53.
    Pandit MK, Sheikh AH, Singh BN (2008) An improved higher order zigzag theory for the static analysis of laminated sandwich plate with soft core. Finite Elem Anal Des 44(9–10):602–610Google Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Faculty of Industrial and Mechanical Engineering, Qazvin BranchIslamic Azad UniversityQazvinIran

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