Advertisement

Arabian Journal for Science and Engineering

, Volume 43, Issue 9, pp 4931–4947 | Cite as

Static and Stability Characteristics of Geometrically Imperfect FGM Plates Resting on Pasternak Elastic Foundation with Microstructural Defect

  • Ankit Gupta
  • Mohammad Talha
Research Article - Mechanical Engineering
  • 51 Downloads

Abstract

The static and stability characteristics of geometrically imperfect functionally graded material (FGM) plate with a microstructural defect (porosity) resting on Pasternak elastic foundation are investigated. The formulations are based on hybrid higher-order shear and normal deformation theory. A new mathematical expression is presented to accomplish the effective material properties of the material with porosity inclusion. A generic function is employed to model various modes of geometric imperfection. The equations of motion are derived using variational principle. Convergence and comparison studies with reported results ensure the reliability and accuracy of the present solution. Influence of geometric imperfection, porosity, foundation parameters, and boundary constraints on the static and stability behavior of FGM plate is examined. The results reflect that the geometric imperfection and porosity have a significant influence on the structural response of FGM plate.

Keywords

Geometric imperfection Porosity FGM Sigmoid law Static Stability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Koizumi, M.: FGM activities in Japan. Compos. Part B Eng. 28(1–2), 1–4 (1997)CrossRefGoogle Scholar
  2. 2.
    Gupta, A.; Talha, M.: Recent development in modeling and analysis of functionally graded materials and structures. Prog. Aerosp. Sci. 79, 1–14 (2015)CrossRefGoogle Scholar
  3. 3.
    Reddy, J.N.: Analysis of functionally graded plates. Int. J. Numer. Methods Eng. 47(1–3), 663–684 (2000)CrossRefMATHGoogle Scholar
  4. 4.
    Ferreira, A.J.M.: Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method. Compos. Struct. 69, 449–457 (2005)CrossRefGoogle Scholar
  5. 5.
    Shariat, B.A.S.; Eslami, M.R.: Buckling of thick functionally graded plates under mechanical and thermal loads. Compos. Struct. 78(3), 433–439 (2007)CrossRefGoogle Scholar
  6. 6.
    Mohammadi, M.; et al.: Levy solution for buckling analysis of functionally graded rectangular plates. Appl. Compos. Mater. 17(2), 81–93 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Saidi, A.R.; et al.: Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained third-order shear deformation plate theory. Compos. Struct. 89(1), 110–119 (2009)CrossRefGoogle Scholar
  8. 8.
    Talha, M.; Singh, B.N.: Thermo-mechanical buckling analysis of finite element modeled functionally graded ceramic-metal plates. Int. J. Appl. Mech. 3(4), 867–880 (2011)CrossRefGoogle Scholar
  9. 9.
    Talha, M.; Singh, B.N.: Static response and free vibration analysis of FGM plates using higher order shear deformation theory. Appl. Math. Model. 34(12), 3991–4011 (2010)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Gupta, A.; et al.: Vibration characteristics of functionally graded material plate with various boundary constraints using higher order shear deformation theory. Compos. Part B Eng. 94, 64–74 (2016)CrossRefGoogle Scholar
  11. 11.
    Gupta, A.; et al.: Natural frequency of functionally graded plates resting on elastic foundation using finite element method. Procedia Technol. 23, 163–170 (2016)CrossRefGoogle Scholar
  12. 12.
    Elishakoff, I.; et al.: Three-dimensional analysis of an all-round clamped plate made of functionally graded materials. Acta Mech. 180(1–4), 21–36 (2005)CrossRefMATHGoogle Scholar
  13. 13.
    Nguyen, T.-K.: A higher-order hyperbolic shear deformation plate model for analysis of functionally graded materials. Int. J. Mech. Mater. Des. 11(2), 203–219 (2015)CrossRefGoogle Scholar
  14. 14.
    Pendhari, S.S.; et al.: Static solutions for functionally graded simply supported plates. Int. J. Mech. Mater. Des. 8(1), 51–69 (2012)CrossRefGoogle Scholar
  15. 15.
    Baltacioglu, A.K.; et al.: Nonlinear static response of laminated composite plates by discrete singular convolution method. Compos. Struct. 93(1), 153–161 (2010)CrossRefGoogle Scholar
  16. 16.
    Lam, K.Y.; et al.: Canonical exact solutions for Levy-plates on two-parameter foundation using Green’s functions. Eng. Struct. 22(4), 364–378 (2000)CrossRefGoogle Scholar
  17. 17.
    Gilhooley, D.F.; et al.: Analysis of thick functionally graded plates by using higher-order shear and normal deformable plate theory and MLPG method with radial basis functions. Compos. Struct. 80(4), 539–552 (2007)CrossRefGoogle Scholar
  18. 18.
    Liew, K.M.; et al.: Differential quadrature method for Mindlin plates on Winkler foundations. Int. J. Mech. Sci. 38(4), 405–421 (1996)CrossRefMATHGoogle Scholar
  19. 19.
    Zhang, D.G.; Zhou, H.M.: Mechanical and thermal post-buckling analysis of FGM rectangular plates with various supported boundaries resting on nonlinear elastic foundations. Thin-Walled Struct. 89, 142–151 (2015)CrossRefGoogle Scholar
  20. 20.
    Sheng, G.G.; Wang, X.: Thermal vibration, buckling and dynamic stability of functionally graded cylindrical shells embedded in an elastic medium. J. Reinf. Plast. Compos. 27(2), 117–134 (2008)CrossRefGoogle Scholar
  21. 21.
    Civalek, Ö.: Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches. Compos. Part B Eng. 50, 171–179 (2013)CrossRefGoogle Scholar
  22. 22.
    Civalek, Ö.; et al.: Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on two-opposite edges. Adv. Eng. Softw. 41(4), 557–560 (2010)CrossRefMATHGoogle Scholar
  23. 23.
    Luo, Y.F.; Teng, J.G.: Stability analysis of shells of revolution on nonlinear elastic foundations. Comput. Struct. 69(4), 499–511 (1998)CrossRefMATHGoogle Scholar
  24. 24.
    Hui, D.; Leissa, A.W.: Effects of geometric imperfections on vibrations of biaxially compressed rectangular flat plates. J. Appl. Mech. 50(4a), 750 (1983)CrossRefMATHGoogle Scholar
  25. 25.
    Hui, D.: Effects of geometric imperfections on frequency–load interaction of biaxially compressed antisymmetric angle ply rectangular plates. J. Appl. Mech. 52(March), 155–162 (1985)CrossRefMATHGoogle Scholar
  26. 26.
    Yang, J.; Huang, X.-L.: Nonlinear transient response of functionally graded plates with general imperfections in thermal environments. Comput. Methods Appl. Mech. Eng. 196(25–28), 2619–2630 (2007)CrossRefMATHGoogle Scholar
  27. 27.
    Librescu, L.; Souza, M.A.: Post-buckling of geometrically imperfect shear-deformable flat panels under combined thermal and compressive edge loadings. J. Appl. Mech. 60(2), 526–533 (1993)CrossRefMATHGoogle Scholar
  28. 28.
    Girish, J.; Ramachandra, L.S.: Thermomechanical postbuckling analysis of symmetric and antisymmetric composite plates with imperfections. Compos. Struct. 67(4), 453–460 (2005)CrossRefGoogle Scholar
  29. 29.
    Lui, T.; Lam, S.S.: Finite strip analysis of laminated plates with general initial imperfection under end shortening. Eng. Struct. 23(6), 673–686 (2001)CrossRefGoogle Scholar
  30. 30.
    Behravan Rad, A.; Shariyat, M.: Thermo-magneto-elasticity analysis of variable thickness annular FGM plates with asymmetric shear and normal loads and non-uniform elastic foundations. Arch. Civ. Mech. Eng. 16(3), 448–466 (2016)CrossRefGoogle Scholar
  31. 31.
    Zhu, J.; et al.: Fabrication of ZrO\(_2\)–NiCr functionally graded material by powder metallurgy. Mater. Chem. Phys. 68(1–3), 130–135 (2001)CrossRefGoogle Scholar
  32. 32.
    Ebrahimi, F.; Mokhtari, M.: Transverse vibration analysis of rotating porous beam with functionally graded microstructure using the differential transform method. J. Braz. Soc. Mech. Sci. Eng. 37(4), 1435–1444 (2015)CrossRefGoogle Scholar
  33. 33.
    Ait Atmane, H.; et al.: Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations. Int. J. Mech. Mater. Des. 13(1), 1–14 (2015)Google Scholar
  34. 34.
    Wattanasakulpong, N.; Ungbhakorn, V.: Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities. Aerosp. Sci. Technol. 32(1), 111–120 (2014)CrossRefGoogle Scholar
  35. 35.
    Magnucka-Blandzi, E.: Non-Linear analysis of dynamic stability of metal foam circular plate. J. Theor. Appl. Mech. 48(1), 207–217 (2010)Google Scholar
  36. 36.
    Yahia, S.A.; et al.: Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories. Struct. Eng. Mech. 53(6), 1143–1165 (2015)CrossRefGoogle Scholar
  37. 37.
    Barati, M.R.; et al.: Buckling analysis of higher order graded smart piezoelectric plates with porosities resting on elastic foundation. Int. J. Mech. Sci. 117, 309–320 (2016)CrossRefGoogle Scholar
  38. 38.
    Ebrahimi, F.; et al.: Free vibration analysis of smart porous plates subjected to various physical fields considering neutral surface position. Arab. J. Sci. Eng. 42(5), 1865–1881 (2017)MathSciNetCrossRefMATHGoogle Scholar
  39. 39.
    Gupta, A.; Talha, M.: Influence of porosity on the flexural and vibration response of gradient plate using nonpolynomial higher-order shear and normal deformation theory. Int J Mech Mater Des. (2017).  https://doi.org/10.1007/s10999-017-9369-2 Google Scholar
  40. 40.
    Gupta, A.; Talha, M.: Influence of porosity on the flexural and free vibration responses of functionally graded plates in thermal environment. Int. J. Struct. Stab. Dyn. 18(1), 1–31 (2018)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Gupta, A.; Talha, M.: An assessment of a non-polynomial based higher order shear and normal deformation theory for vibration response of gradient plates with initial geometric imperfections. Compos. Part B 107, 141–161 (2016)CrossRefGoogle Scholar
  42. 42.
    Grover, N.; et al.: Analytical and finite element modeling of laminated composite and sandwich plates: an assessment of a new shear deformation theory for free vibration response. Int. J. Mech. Sci. 67, 89–99 (2013)CrossRefGoogle Scholar
  43. 43.
    Kitipornchai, S.; et al.: Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections. Int. J. Solids Struct. 41(9–10), 2235–2257 (2004)CrossRefMATHGoogle Scholar
  44. 44.
    Thai, H.-T.; Choi, D.-H.: Analytical solutions of refined plate theory for bending, buckling and vibration analyses of thick plates. Appl. Math. Model. 37(18), 8310–8323 (2013)MathSciNetCrossRefGoogle Scholar
  45. 45.
    Reddy, J.N.: A refined nonlinear theory of plates with transverse shear deformation. Int. J. Solids Struct. 20(9), 881–896 (1984)CrossRefMATHGoogle Scholar
  46. 46.
    Thai, H.-T.; Kim, S.-E.: Closed-form solution for buckling analysis of thick functionally graded plates on elastic foundation. Int. J. Mech. Sci. 75, 34–44 (2013)CrossRefGoogle Scholar
  47. 47.
    Malekzadeh, P.; et al.: Buckling analysis of functionally graded arbitrary straight-sided quadrilateral plates on elastic foundations. Meccanica 47(2), 321–333 (2012)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.Indian Institute of Technology MandiMandiIndia

Personalised recommendations