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Numerical prediction of thermal buckling load parameters of damaged polymeric layered composite structure and reversal of strength using SMA fibre

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Abstract

The thermal buckling load factors of damaged (crack) laminated composite structures have been investigated numerically first-hand. Their strength reversal due to the functional material reinforcement under the elevated environmental conditions is reported in detail. In this regard, a generic finite element model of the damaged layered structure has been derived in the higher-order kinematic model considering the Green–Lagrange type of strain (to count the large deformation due to temperature). Further, the shape memory alloy (SMA) fibre effect has been introduced in the proposed mathematical model via marching technique under the change in temperature to achieve the modified elastic property. The final governing equation of buckled structure has been derived and solved through isoparametric finite element steps. The final buckling temperatures of the damaged layered structural system with and without SMA (volume fraction and prestrain) fibres were obtained, and the results indicate a good improvement (maximum up to 37%). Additionally, the structural geometry-related parameters, including their shapes, have been changed to show the model's applicability.

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Abbreviations

ΔT cr :

Critical buckling temperature

ρ :

Density

\(u_{{1\xi_{{\text{x}}} }}\) \(u_{{1\xi_{{\text{y}}} }}\) and \(u_{{1\xi_{{\text{z}}} }}\) :

Displacement at mid-plane

\(\left\{ \lambda \right\},\left\{ {\dot{\lambda }} \right\}\) and \(\left\{ {\ddot{\lambda }} \right\}\) :

Displacement, velocity, and acceleration

\(\left\{ \Delta \right\}\) :

Eigenvector

\(\left\{ {\delta_{0} } \right\}\) and \(\left\{ {\delta_{{{\text{oi}}}} } \right\}\) :

Elemental and nodal displacement

\([K_{{G_{{{\text{ther}}}} }} ]^{{{\text{elm}}}}\) and \([K_{{G_{{{\text{rec}}}} }} ]^{{{\text{elm}}}}\) :

Elemental geometric stiffness matrix of thermal and recovery stresses

\(\theta\) :

Fibre orientation angle

\(\{ \overline{\varepsilon }_{{\text{G}}} \}\) :

Geometric strain vector

\(\left[ {K_{{\text{G}}} } \right]\) :

Geometrical stiffness matrix

\(U_{{\xi {\text{x}}}}\), \(U_{{\xi {\text{y}}}}\) and \(U_{{\xi {\text{z}}}}\) :

Global displacement

\(\xi_{{\text{x}}} ,\;\xi_{{\text{y}}}\) and \(\xi_{{\text{z}}}\) :

Global reference axis of the shell panel

\(u_{{3\xi_{{\text{x}}} }}\) \(u_{{3\xi_{{\text{y}}} }}\) \(u_{{4\xi_{{\text{x}}} }}\) and \(u_{{4\xi_{{\text{y}}} }}\) :

Higher-order deformation parameters

l, b, and h :

Length, width, and depth of laminated shell panel

\(\left[ M \right]\) :

Mass matrix

\(\left[ {D_{{G_{{{\text{rec}}}} }} } \right]\) and \(\left[ {D_{{G_{{{\text{ther}}}} }} } \right]\) :

Material property matrix w.r.t recovery and thermal load

\(\left\{ {f_{{{\text{mech}}}} } \right\}\), \(\left\{ {f_{{{\text{ther}}}} } \right\}\) and \(\left\{ {f_{{{\text{rec}}}} } \right\}\) :

Mechanical load, thermal load, and the recovery load vector

n l :

Number of layers in the composite

v :

Poison’s ratio

\(u_{{2\xi_{{\text{x}}} }}\) and \(u_{{2\xi_{{\text{y}}} }}\) :

Rotation along \(\xi_{{\text{x}}} ,\;\xi_{{\text{y}}}\)

\(N\) :

Shape function

G 11, G 12, G 23 :

Shear modulus

\(\left[ K \right]\) :

Stiffness matrix

\(\varepsilon\) and ε r :

Strain and prestrain

\(\left[ B \right]\) and \(\left[ {B_{{\text{G}}} } \right]\) :

Strain displacement matrix

\(\sigma_{{{\text{rec}}}}\) and \(\sigma_{{{\text{ther}}}}\) :

Stresses due to recovery and thermal load.

\(\Delta T\) :

Temperature difference

\(\alpha\) :

Thermal expansion coefficient

\(\{ U\}\) :

Total strain energy

\(\Delta W_{{{\text{tot}}}}\) :

Total work done

\(V_{{f_{{{\text{SMA}}}} }}\)/V f :

Volume fraction of SMA

E 11, E 12, E 23 :

Young’s modulus values

References

  1. Thornton, E.A.: Thermal buckling of plates and shells. Appl. Mech. Rev. 46, 485–506 (1993). https://doi.org/10.1115/1.3120310

    Article  Google Scholar 

  2. Chang, J.-S., Leu, S.-Y.: Thermal buckling analysis of antisymmetric angle-ply laminates based on a higher-order displacement field. Compos. Sci. Technol. 41, 109–128 (1991). https://doi.org/10.1016/0266-3538(91)90023-I

    Article  Google Scholar 

  3. Chandrashekhara, K.: Thermal buckling of laminated plates using a shear flexible finite element. Finite Elem. Anal. Des. 12, 51–61 (1992). https://doi.org/10.1016/0168-874X(92)90006-X

    Article  MATH  Google Scholar 

  4. Naghsh, A., Azhari, M., Saadatpour, M.M.: Thermal buckling analysis of point-supported laminated composite plates in unilateral contact. Appl. Math. Model. 56, 564–583 (2018). https://doi.org/10.1016/j.apm.2017.12.020

    Article  MathSciNet  MATH  Google Scholar 

  5. Lakshmi Narayana, A., Vijaya Kumar, R., Krishnamohana Rao, G.: Effect of volume fraction on the thermal buckling analysis of laminated composite plate with square/rectangular cutout. Mater. Today Proc. 5, 5819–5829 (2018). https://doi.org/10.1016/j.matpr.2017.12.179

    Article  Google Scholar 

  6. Lakshmi Narayana, A., Vijaya Kumar, R., Krishnamohana Rao, G.: Thermal buckling analysis of laminated composite plate with square/rectangular. Elliptical/Circular Cutout. Mater. Today Proc. 5, 5354–5363 (2018). https://doi.org/10.1016/j.matpr.2017.12.121

    Article  Google Scholar 

  7. Baseri, V., Jafari, G.S., Kolahchi, R.: Analytical solution for buckling of embedded laminated plates based on higher order shear deformation plate theory. Steel Compos. Struct. 21(4), 883–919 (2016). https://doi.org/10.12989/scs.2016.21.4.883

    Article  Google Scholar 

  8. Akbaş, ŞD.: Post-buckling analysis of a fiber reinforced composite beam with crack. Eng. Fract. Mech. 212, 70–80 (2019). https://doi.org/10.1016/j.engfracmech.2019.03.007

    Article  Google Scholar 

  9. Sadeghifar, M., Bagheri, M., Jafari, A.A.: Buckling analysis of stringer-stiffened laminated cylindrical shells with nonuniform eccentricity. Arch. Appl. Mech. 81, 875–886 (2011). https://doi.org/10.1007/s00419-010-0457-0

    Article  MATH  Google Scholar 

  10. Shimamoto, A., Ohkawara, H., Nogata, F.: Enhancement of mechanical strength by shape memory effect in TiNi fiber-reinforced composites. Eng. Fract. Mech. 71, 737–746 (2004). https://doi.org/10.1016/S0013-7944(03)00052-3

    Article  Google Scholar 

  11. Lee, H.J., Lee, J.J., Huh, J.S.: A simulation study on the thermal buckling behavior of laminated composite shells with embedded shape memory alloy (SMA) wires. Compos. Struct. 47, 463–469 (1999). https://doi.org/10.1016/S0263-8223(00)00020-9

    Article  Google Scholar 

  12. Tawfik, M., Ro, J.J., Mei, C.: Thermal post-buckling and aeroelastic behaviour of shape memory alloy reinforced plates. Smart Mater. Struct. 11, 297–307 (2002). https://doi.org/10.1088/0964-1726/11/2/313

    Article  Google Scholar 

  13. Park, J.-S., Kim, J.-H., Moon, S.-H.: Thermal post-buckling and flutter characteristics of composite plates embedded with shape memory alloy fibers. Compos. Part B Eng. 36, 627–636 (2005). https://doi.org/10.1016/j.compositesb.2004.11.007

    Article  Google Scholar 

  14. Kumar, S.K., Singh, B.N.: Thermal buckling analysis of SMA fiber-reinforced composite plates using layerwise model. J. Aerosp. Eng. 22, 342–353 (2009). https://doi.org/10.1061/(ASCE)0893-1321(2009)22:4(342)

    Article  Google Scholar 

  15. Kumar, C.N., Singh, B.N.: Thermal buckling and post-buckling of laminated composite plates with SMA fibers using layerwise theory. Int. J. Comput. Methods Eng. Sci. Mech. 10, 423–429 (2009). https://doi.org/10.1080/15502280903108024

    Article  MathSciNet  MATH  Google Scholar 

  16. Panda, S.K., Singh, B.N.: Thermal post-buckling analysis of a laminated composite spherical shell panel embedded with shape memory alloy fibres using non-linear finite element method. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 224, 757–769 (2010). https://doi.org/10.1243/09544062JMES1809

    Article  Google Scholar 

  17. Kamarian, S., Shakeri, M.: Thermal buckling analysis and stacking sequence optimization of rectangular and skew shape memory alloy hybrid composite plates. Compos. Part B Eng. 116, 137–152 (2017). https://doi.org/10.1016/j.compositesb.2017.01.059

    Article  Google Scholar 

  18. Manickam, G., Bharath, A., Das, A.N., Chandra, A., Barua, P.: Thermal buckling behaviour of variable stiffness laminated composite plates. Mater. Today Commun. 16, 142–151 (2018). https://doi.org/10.1016/j.mtcomm.2018.05.003

    Article  Google Scholar 

  19. Torabi, J., Ansari, R., Hassani, R.: Numerical study on the thermal buckling analysis of CNT-reinforced composite plates with different shapes based on the higher-order shear deformation theory. Eur. J. Mech. A/Solids. 73, 144–160 (2019). https://doi.org/10.1016/j.euromechsol.2018.07.009

    Article  MathSciNet  MATH  Google Scholar 

  20. Civalek, Ö., Dastjerdi, S., Akgöz, B.: Buckling and free vibrations of CNT-reinforced cross-ply laminated composite plates. Mech. Based Des. Struct. Mach. 50, 1914–1931 (2022). https://doi.org/10.1080/15397734.2020.1766494

    Article  Google Scholar 

  21. Kamarian, S., Bodaghi, M., Isfahani, R.B., Song, J.: A comparison between the effects of shape memory alloys and carbon nanotubes on the thermal buckling of laminated composite beams. Mech. Based Des. Struct. Mach. (2020). https://doi.org/10.1080/15397734.2020.1776131

    Article  Google Scholar 

  22. Soleimanian, S., Davar, A., Eskandari Jam, J., Zamani, M.R., Heydari Beni, M.: Thermal buckling and thermal induced free vibration analysis of perforated composite plates: a mathematical model. Mech. Adv. Compos. Struct. 7, 15–23 (2020). https://doi.org/10.22075/macs.2019.16556.1181

    Article  Google Scholar 

  23. Devarajan, B., Kapania, R.K.: Thermal buckling of curvilinearly stiffened laminated composite plates with cutouts using isogeometric analysis. Compos. Struct. 238, 111881 (2020). https://doi.org/10.1016/j.compstruct.2020.111881

    Article  Google Scholar 

  24. Shojaee, S., Valizadeh, N., Izadpanah, E., Bui, T., Vu, T.-V.: Free vibration and buckling analysis of laminated composite plates using the NURBS-based isogeometric finite element method. Compos. Struct. 94, 1677–1693 (2012). https://doi.org/10.1016/j.compstruct.2012.01.012

    Article  Google Scholar 

  25. Arani, A.G., Maghamikia, S., Mohammadimehr, M., Arefmanesh, A.: Buckling analysis of laminated composite rectangular plates reinforced by SWCNTs using analytical and finite element methods. J. Mech. Sci. Technol. 25, 809–820 (2011). https://doi.org/10.1007/s12206-011-0127-3

    Article  Google Scholar 

  26. Rasid, Z.A., Ayob, A., Zahari, R., Mustapha, F., Majid, D.L., Varatharajoo, R.: Thermal buckling and post-buckling improvements of laminated composite plates using finite element method. Key Eng. Mater. 471–472, 536–541 (2011). https://doi.org/10.4028/www.scientific.net/KEM.471-472.536

    Article  Google Scholar 

  27. Safaei, B.: Frequency-dependent damped vibrations of multifunctional foam plates sandwiched and integrated by composite faces. Eur. Phys. J. Plus. 136, 646 (2021). https://doi.org/10.1140/epjp/s13360-021-01632-4

    Article  Google Scholar 

  28. Safaei, B.: The effect of embedding a porous core on the free vibration behavior of laminated composite plates. Steel Compos. Struct. 35, 659–670 (2020). https://doi.org/10.12989/scs.2020.35.5.641

    Article  Google Scholar 

  29. Atilla, D., Sencan, C., Goren Kiral, B., Kiral, Z.: Free vibration and buckling analyses of laminated composite plates with cutout. Arch. Appl. Mech. 90, 2433–2448 (2020). https://doi.org/10.1007/s00419-020-01730-2

    Article  Google Scholar 

  30. Asadi, H., Eynbeygi, M., Wang, Q.: Nonlinear thermal stability of geometrically imperfect shape memory alloy hybrid laminated composite plates. Smart Mater. Struct. 23, 075012 (2014). https://doi.org/10.1088/0964-1726/23/7/075012

    Article  Google Scholar 

  31. Nasirmanesh, A., Mohammadi, S.: Eigenvalue buckling analysis of cracked functionally graded cylindrical shells in the framework of the extended finite element method. Compos. Struct. 159, 548–566 (2017). https://doi.org/10.1016/j.compstruct.2016.09.065

    Article  Google Scholar 

  32. Nasirmanesh, A., Mohammadi, S.: XFEM buckling analysis of cracked composite plates. Compos. Struct. 131, 333–343 (2015). https://doi.org/10.1016/j.compstruct.2015.05.013

    Article  Google Scholar 

  33. Xu, C., Rong, D., Zhou, Z., Deng, Z., Lim, C.W.: Vibration and buckling characteristics of cracked natural fiber reinforced composite plates with corner point-supports. Eng. Struct. 214, 110614 (2020). https://doi.org/10.1016/j.engstruct.2020.110614

    Article  Google Scholar 

  34. Rostamijavanani, A., Ebrahimi, M.R., Jahedi, S.: Thermal post-buckling analysis of laminated composite plates embedded with shape memory alloy fibers using semi-analytical finite strip method. J. Fail. Anal. Prev. 21, 290–301 (2020). https://doi.org/10.1007/s11668-020-01068-5

    Article  Google Scholar 

  35. Liu, Y., Qin, Z., Chu, F.: Nonlinear forced vibrations of rotating cylindrical shells under multi-harmonic excitations in thermal environment. Nonlinear Dyn. 108, 2977–2991 (2022). https://doi.org/10.1007/s11071-022-07449-9

    Article  Google Scholar 

  36. Li, H., Siqi, Z., Shi, X., Wu, H., Zhaoye, Q., Pengxu, L., Wang, X., Zhongwei, G.: Thermal-vibration aging of fiber-reinforced polymer cylindrical shells with polyurea coating: theoretical and experimental studies. Mech. Adv. Mater. Struct. (2022). https://doi.org/10.1080/15376494.2022.2032886

    Article  Google Scholar 

  37. Li, H., Lv, H., Gu, J., **ong, J., Han, Q., Liu, J., Qin, Z.: Nonlinear vibration characteristics of fibre reinforced composite cylindrical shells in thermal environment. Mech. Syst. Signal Process. 156, 107665 (2021). https://doi.org/10.1016/j.ymssp.2021.107665

    Article  Google Scholar 

  38. Liu, Y., Qin, Z., Chu, F.: Nonlinear forced vibrations of functionally graded piezoelectric cylindrical shells under electric-thermo-mechanical loads. Int. J. Mech. Sci. 201, 106474 (2021). https://doi.org/10.1016/j.ijmecsci.2021.106474

    Article  Google Scholar 

  39. Bassi, M.A., Lopez, M.A., Confalone, L., Gaudio, R.M., Lombardo, L., Lauritano, D.: Enhanced Reader.pdf (2020)

  40. Mehar, K., Panda, S.K., Dehengia, A., Kar, V.R.: Vibration analysis of functionally graded carbon nanotube reinforced composite plate in thermal environment. J. Sandw. Struct. Mater. 18, 151–173 (2016). https://doi.org/10.1177/1099636215613324

    Article  Google Scholar 

  41. Dewangan, H.C., Sharma, N., Hirwani, C.K., Panda, S.K.: Numerical eigenfrequency and experimental verification of variable cutout (square/rectangular) borne layered glass/epoxy flat/curved panel structure. Mech. Based Des. Struct. Mach. (2020). https://doi.org/10.1080/15397734.2020.1759432

    Article  Google Scholar 

  42. Erukala, K.K., Mishra, P.K., Dewangan, H.C., Panda, S.K., Dwivedi, M.: Damaged composite structural strength enhancement under elevated thermal environment using shape memory alloy fiber. Acta Mech. 233, 3133–3155 (2022). https://doi.org/10.1007/s00707-022-03272-w

    Article  MathSciNet  MATH  Google Scholar 

  43. Cook, R.D., Malkus, D.S., Plesha, M.E., W.R.: Concepts and Applications of Finite Element Analysis. Willy, Singapore (2003)

    Google Scholar 

  44. Duan, B., Tawfik, M., Goek, S.N., Ro, J.-J., Mei, C.: Analysis and control of large thermal deflection of composite plates using shape memory alloy. Smart Struct. Mater. 2000 Ind. Commer. Appl. Smart Struct. Technol. 3991, 358–365 (2000). https://doi.org/10.1117/12.388178

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology Rourkela, Rourkela, 769008, India

    Erukala Kalyan Kumar & Subrata Kumar Panda

  2. School of Mechanical Engineering, KIIT, Bhubaneswar, Odisha, India

    Nitin Sharma

  3. GRC Department, Applied College, King Abdulaziz University, Jeddah, 2158, Saudi Arabia

    S. R. Mahmoud

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Kumar, E.K., Sharma, N., Panda, S.K. et al. Numerical prediction of thermal buckling load parameters of damaged polymeric layered composite structure and reversal of strength using SMA fibre. Arch Appl Mech 92, 3829–3845 (2022). https://doi.org/10.1007/s00419-022-02265-4

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