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Static and dynamic nonlinear stability analyses of hybrid sandwich composite beams under variable in-plane loads

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Abstract

Post-buckling and dynamic nonlinear stability analyses of a sandwich functionally graded material (FGM) composite beam subject to in-plane compressive static and periodic loading are conducted by implementing a higher-order shear deformation with von Karman kinematics. The dynamic instability region is evaluated using the Mathieu-Hill-type equation in Bolotin’s method. Comparisons of the layered composite beam, FGM sandwich composite beam, shape memory polymer (SMP) composite beam, and SMP-FGM sandwich composite beam with variable in-plane loads \((N_x^1, N_x^2, N_x^3)\) are depicted for the first time in the current work. The unstable region of \(N_x^3\) is lower compared with those of \(N_x^1\) and \(N_x^2\).

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References

  1. N. D. Duc, Nonlinear dynamic response of imperfect eccentrically stiffened FGM double curved shallow shells on elastic foundation, J. Composite Structures, 99 (2013) 88–96.

    Article  Google Scholar 

  2. A. Karamanli and M. Aydogdu, Buckling of laminated composite and sandwich beams due to axially varying in-plane loads, Composite Structures, 210 (2019) 391–408.

    Article  Google Scholar 

  3. R. K. Gupta, J. B. Gunda, G. R. Janardhan and G. V. Rao, Post-buckling analysis of composite beams: simple and accurate closed-form expressions, Composite Structures, 92(8) (2010) 1947–1956.

    Article  Google Scholar 

  4. S. D. Akbas, Hygrothermal post-buckling analysis of laminated composite beams, International Journal of Applied Mechanics, 11(1) (2019) 1950009.

    Article  MathSciNet  Google Scholar 

  5. S. J. Song and A. M. Waas, Effects of shear deformation on buckling and free vibration of laminated composite beams, Composite Structures, 37(1) (1997) 3343.

    Article  Google Scholar 

  6. J. Lee, S. E. Kim and K. Hong, Lateral buckling of i-section composite beams, Engineering Structures, 24(7) (2002) 955964.

    Article  Google Scholar 

  7. S. K. Singh and A. Chakrabarti, Buckling analysis of laminated composite plates using an efficient C0 FE model, A. Lat. Am. J. Solids Struct., 9(3) (2012) 1–13.

    Article  Google Scholar 

  8. M. K. Ranganatha Swamy, U. S. Mallikarjun and V. Udayakumar, Synthesis and characterization of shape memory polymers, IOP MSE, 577 (2019) 012095.

    Google Scholar 

  9. D. W. Hanzon, K. Yu and C. M. Yakacki, Chapter 5 — active mechanisms of shape-memory polymers, Shape-Memory Polymer Device Design, William Andrew Publishing (2017) 139–187.

  10. D. M. Feldkamp and I. A. Rousseau, Effect of the deformation temperature on the shape-memory behavior of epoxy networks, Macromolecular Materials and Engineering, 295(8) (2010) 726–734.

    Article  Google Scholar 

  11. J. Leng, L. Xin, Y. Liu and S. Du, Shape-memory polymers and their composites: stimulus methods and applications, Progress in Materials Science, 56(7) (2011) 1077–1135.

    Article  Google Scholar 

  12. C. S. Zhang and Q. Q. Ni, Bending behavior of shape memory polymer based laminates, Composite Structures, 78(2) (2007) 153–161.

    Article  Google Scholar 

  13. A. Lal and K. Markad, Influence of dynamic temperature variation and inplane varying loads over post-buckling and free vibration analysis of sandwich composite beam, International Journal of Computational Materials Science and Engineering, 9(3) (2020) 2050012.

    Article  Google Scholar 

  14. G. A. Zizicas, Dynamic buckling of thin plates, Trans. ASME, 74(7) (1952) 1257–1268.

    Google Scholar 

  15. L. Librescu and N. K. Chandiramani, Dynamic stability of transversely isotropic viscoelastic plates, Journal of Sound and Vibration, 130(3) (1989) 467–486.

    Article  MATH  Google Scholar 

  16. H. Ozturk and M. Sabuncu, Stability analysis of a cantilever composite beam on elastic supports, Composites Science and Technology, 65 (2005) 1982–1995.

    Article  Google Scholar 

  17. M. Touratier, An efficient standard plate theory, International Journal of Engineering Science, 29 (1991) 901–916.

    Article  MATH  Google Scholar 

  18. A. Beakou and M. Touratier, A rectangular plate finite element for analysing composite multilayered shallow shell in statics, vibration and buckling, International Journal for Numerical Methods in Engineering, 36 (1993) 627–653.

    Article  MATH  Google Scholar 

  19. M. A. R. Loja, J. I. Barbosa and C. M. M. Soares, Static and dynamic behaviour of laminated composite beams, International Journal of Structural Stability and Dynamics, 1(4) (2001) 545–560.

    Article  Google Scholar 

  20. G. K. Binnur, Static and dynamic stability analyses of the symmetric laminated cantilever beams, Advanced Composites Letters, 17 (5) (2008).

  21. C. Karaagac, H. Ozturk and M. Sabuncu, Lateral dynamic stability analysis of a cantilever laminated composite beam with an elastic support, International Journal of Structural Stability and Dynamics, 7(3) (2007) 377–402.

    Article  Google Scholar 

  22. N. V. Thanh, N. D. Khoa, N. D. Tuan, P. Tran and N. D. Duc, Nonlinear dynamic response and vibration of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) shear deformable plates with temperature dependence material properties and surrounded on elastic foundations, J. Thermal Stresses, 40–10 (2017) 1254–1274.

    Article  Google Scholar 

  23. Y. Fu, J. Wang and Y. Mao, Nonlinear analysis of buckling, free vibration and dynamic stability for the piezoelectric functionally graded beams in thermal environment, Appl. Math. Model., 36(9) (2012) 4324–4340.

    Article  MathSciNet  MATH  Google Scholar 

  24. N. D. Duc, T. Q. Quan and V. D. Luat, Nonlinear dynamic analysis and vibration of shear deformable piezoelectric FGMdouble curved shallow shells under damping-thermoelectro-mechanical loads, J. Composite Structures, 125 (2015) 29–40.

    Article  Google Scholar 

  25. H. S. Shen, Thermal postbuckling behavior of shear deformable FGM plates with temperature-dependent properties, Int. J. Mech. Sci., 49(4) (2007) 466–478.

    Article  Google Scholar 

  26. H. S. Shen, Postbuckling of FGM plates with piezoelectric actuators under thermo-electro-mechanical loadings, Int. J. Solids Struct., 42(23) (2005) 6101–6121.

    Article  MATH  Google Scholar 

  27. F. A. Fazzolari, Stability analysis of FGM sandwich plates by using variable-kinematics Ritz models, Mechanics of Advanced Materials and Structures, 23(9) (2016) 1104–1113.

    Article  Google Scholar 

  28. M. Zamanzadeh, G. Rezazadeh, I. Jafarsadeghipoornaki and R. Shabani, Static and dynamic stability modeling of a capacitive FGM micro-beam in presence of temperature changes, Applied Mathematical Modelling, 37(10–11) (2013) 6964–6978.

    Article  MathSciNet  MATH  Google Scholar 

  29. L. C. Trinh, T. P. Vo, H. T. Thai and T. K. Nguyen, Size dependent vibration of bi-directional functionally graded micro-beams with arbitrary boundary conditions, Composites Part B: Engineering, 134 (2018) 225–245.

    Article  Google Scholar 

  30. N. D. Duc, Nonlinear thermo-electro-mechanical dynamic response of shear deformable piezoelectric sigmoid functionally graded sandwich circular cylindrical shells on elastic foundations, Journal of Sandwich Structures and Materials, 20(3) (2016) 351–378.

    Google Scholar 

  31. N. D. Duc, Nonlinear Static and Dynamic Stability of Functionally Graded Plates and Shells, Vietnam National University Press, Hanoi (2014).

    Google Scholar 

  32. N. V. Thanh, V. D. Quang, N. D. Khoa, S. E. Kim and N. D. Duc, Nonlinear dynamic response and vibration of FG CNTRC shear deformable circular cylindrical shell with temperature dependent material properties and surrounded on elastic foundations, Journal of Sandwich Structures and Materials, 21(7) (2018) 2456–2483.

    Article  Google Scholar 

  33. N. D. Duc and P. D. Nguyen, The dynamic response and vibration of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) truncated conical shells resting on elastic foundation, Materials, 10 (2017) 1194.

    Article  Google Scholar 

  34. P. H. Cong, N. D. Khanh, N. D. Khoa and N. D. Duc, New approach to investigate nonlinear dynamic response of sandwich auxetic double curves shallow shells using TSDT, Composite Structures, 185 (2018) 455–465.

    Article  Google Scholar 

  35. N. D. Duc, T. Q. Quan and N. D. Khoa, New approach to investigate nonlinear dynamic response and vibration of imperfect functionally graded carbon nanotube reinforced composite double curved shallow shells subjected to blast load and temperature, Journal Aerospace Science and Technology, 71 (2017) 360–372.

    Article  Google Scholar 

  36. T. Q. Quan and N. D. Duc, Nonlinear thermal stability of eccentrically stiffened FGM double curved shallow shells, J. Thermal Stresses, 40(2) (2016) 211–236.

    Article  Google Scholar 

  37. N. D. Duc, S. E. Kim, P. H. Cong, N. T. Anh and N. D. Khoa, Dynamic response and vibration of composite double curved shallow shells with negative poisson’s ratio in auxetic honeycombs core layer on elastic foundations subjected to blast and damping loads, International Journal of Mechanical Sciences, 133 (2017) 504–512.

    Article  Google Scholar 

  38. V. T. T. Anh and N. D. Duc, Nonlinear response of shear deformable S-FGM shallow spherical shell with ceramic-metal-ceramic layers resting on elastic foundation in thermal environment, J. Mechanics of Advanced Materials and Structures, 23(8) (2015) 926–934.

    Article  Google Scholar 

  39. N. D. Duc and T. Q. Quan, Nonlinear dynamic analysis of imperfect FGM double curved thin shallow shells with temperature-dependent properties on elastic foundation, Journal of Vibration and Control, 21(7) (2013) 1340–1362.

    Article  Google Scholar 

  40. K. K. Westbrook, P. H. Kao, F. Castro, Y. Ding and H. J. Qi, A 3D finite deformation constitutive model for amorphous shape memory polymers: a multi-branch modeling approach for non-equilibrium relaxation processes, Mechanics of Materials, 43 (2011) 853–869.

    Article  Google Scholar 

  41. J. Gu, J. Leng and H. Sun, A constitutive model for amorphous shape memory polymers based on thermodynamics with internal state variables, Mechanics of Materials, 111 (2017) 1–14.

    Article  Google Scholar 

  42. J. Gu, J. Leng, H. Sun, H. Zeng and Z. Cai, Thermomechanical constitutive modeling of fiber reinforced shape memory polymer composites based on thermodynamics with internal state variables, Mechanics of Materials, 130 (2019) 9–19.

    Article  Google Scholar 

  43. C. A. Mahieux and K. L. Reifsnider, Property modeling across transition temperatures in polymers: a robust stiffness-temperature model, Polymer, 42(7) (2001) 3281–3291.

    Article  Google Scholar 

  44. H. J. Qi, T. D. Nguyen, F. Castro, C. M. Yakacki and R. Shandas, Finite deformation thermo-mechanical behavior of thermally induced shape memory polymers, Journal of the Mechanics and Physics of Solids, 56(5) (2008) 1730–1751.

    Article  MATH  Google Scholar 

  45. P. R. Heyliger and J. N. Reddy, A higher order beam finite element for bending and vibration problems, J. Sound Vib., 126(2) (1988) 309–326.

    Article  MATH  Google Scholar 

  46. S. C. Mohanty, R. R. Dash and T. Rout, Static and dynamic stability analysis of a functionally graded Timoshenko beam, International Journal of Structural Stability and Dynamics, 12(4) (2012) 1250025.

    Article  MathSciNet  MATH  Google Scholar 

  47. A. Lal, N. M. Kulkarni and B. N. Singh, Stochastic thermal post buckling response of elastically supported laminated piezoelectric composite plate using micromechanical approach, Curv. Layer. Struct., 2 (2015) 331–350.

    Google Scholar 

  48. J. N. Reddy, Mechanics of Laminated Composite Plates Theory and Analysis, CRS Press, New York (1997).

    MATH  Google Scholar 

  49. J. R. Kumpfer and S. J. Rowan, Thermo-, photo-, and chemoresponsive shape-memory properties from photo-cross-linked metallo-supramolecular polymers, J. Am. Chem. Soc., 133 (2011) 12866–12874.

    Article  Google Scholar 

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Correspondence to Kanif Markad.

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Kanif M. Markad was born in Ahmednagar, Maharashtra, India, in 1987. He received Bachelor’s degree in Mechanical Engineering from Pune University, Master’s degree in Design Engineering from Solapur University and presently working as a Research Scholar in Mechanical Engineering Department, SVNIT, Surat, India. His main research interest includes numerical analysis of composite materials, smart materials, manufacturing and analysis of smart hybrid materials.

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Lal, A., Markad, K. Static and dynamic nonlinear stability analyses of hybrid sandwich composite beams under variable in-plane loads. J Mech Sci Technol 35, 3895–3908 (2021). https://doi.org/10.1007/s12206-021-0803-x

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  • DOI: https://doi.org/10.1007/s12206-021-0803-x

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