Advertisement

Post-buckling analysis of FGM plates under in-plane mechanical compressive loading by using a mesh-free approximation

  • Vuong Nguyen Van Do
  • Kyong-Ho Chang
  • Chin-Hyung LeeEmail author
Original
  • 30 Downloads

Abstract

This study introduces an accurate and effective mesh-free approximation based on the radial point interpolation method (RPIM) to predict the post-buckling responses of FGM plates in mechanical edge compression. In the RPIM, a new radial basis function is presented in a compactly supported form to build the shape functions without any fitting parameters. The equilibrium and governing equations for the plate are derived by using the higher-order shear deformation theory in which a new hybrid type transverse shear function is incorporated in order to better represent the displacement fields. A von Kármán type nonlinear equation which accounts for both the geometric nonlinearity and the initial geometric imperfection is constructed. A solution procedure based on the total Lagrangian formulation to trace the post-buckling path, which utilizes the modified Newton–Raphson method, is designed. The numerical results illustrate the accuracy of the proposed meshless method for predicting the post-buckling behavior of FGM plates.

Keywords

Post-buckling Geometric imperfection Higher-order shear deformation theory Mesh-free method Radial point interpolation 

Notes

Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 107.02-2018.28.

References

  1. 1.
    Wang, X., Lu, G., Xiao, D.: Non-linear thermal buckling for local delamination near the surface of laminated cylindrical shell. Int. J. Mech. Sci. 44, 947–965 (2002)CrossRefzbMATHGoogle Scholar
  2. 2.
    Koizumu, K.: The concept of FGM, ceramic transactions. Funct. Grad. Mater. 34, 3–10 (1993)Google Scholar
  3. 3.
    Birman, V., Byrd, L.W.: Modeling and analysis of functionally graded materials and structures. ASME Appl. Mech. Rev. 60, 195–216 (2007)CrossRefGoogle Scholar
  4. 4.
    Swaminathan, K., Naveenkumar, D.T., Zenkour, A.M., Carrera, E.: Stress, vibration and buckling analyses of FGM plates: a state-of-the-art review. Compos. Struct. 120, 10–31 (2015)CrossRefGoogle Scholar
  5. 5.
    Swaminathan, K., Sangeetha, D.M.: Thermal analysis of FGM plates: a critical review of various modeling techniques and solution methods. Compos. Struct. 160, 43–60 (2017)CrossRefGoogle Scholar
  6. 6.
    Feldman, E., Aboudi, J.: Buckling analysis of functionally graded plates subjected to uniaxial loading. Compos. Struct. 38, 29–36 (1997)CrossRefGoogle Scholar
  7. 7.
    Javaheri, R., Eslami, M.R.: Buckling of functionally graded plates under in-plane compressive loading. Z. Angew Math. Mech. 82, 277–283 (2002)CrossRefzbMATHGoogle Scholar
  8. 8.
    Najafizadeh, M.M., Eslami, M.R.: Buckling analysis of circular plates of functionally graded materials under uniform radial compression. Int. J. Mech. Sci. 44, 2474–2493 (2002)CrossRefzbMATHGoogle Scholar
  9. 9.
    Lanhe, W.: Thermal buckling of a simply supported moderately thick rectangular FGM plate. Compos. Struct. 64, 211–218 (2004)CrossRefGoogle Scholar
  10. 10.
    Na, K.S., Kim, J.H.: Three-dimensional thermomechanical buckling analysis of functionally graded composite plates. Compos. Struct. 73, 413–422 (2006)CrossRefGoogle Scholar
  11. 11.
    Zhao, X., Lee, Y.Y., Liew, K.M.: Mechanical and thermal buckling analysis of functionally graded plates. Compos. Struct. 90, 161–171 (2009)CrossRefGoogle Scholar
  12. 12.
    Lee, Y.H., Bae, S.I., Kim, J.H.: Thermal buckling behavior of functionally graded plates based on neutral surface. Compos. Struct. 137, 208–214 (2016)CrossRefGoogle Scholar
  13. 13.
    Liew, K.M., Yang, J., Kittipornchai, S.: Postbuckling of piezoelectric FGM plates subjected to thermo-electro-mechanical loading. Int. J. Solids Struct. 40, 3689–3892 (2003)Google Scholar
  14. 14.
    Woo, J., Meguid, S.A., Liew, K.M.: Thermomechanical postbuckling analysis of functionally graded plates and shallow cylindrical shells. Acta Mech. 165, 99–115 (2003)CrossRefzbMATHGoogle Scholar
  15. 15.
    Yang, J., Shen, H.S.: Non-linear analysis of functionally graded plates under transverse and in-plane loads. Int. J. Nonlinear Mech. 38, 467–482 (2003)CrossRefzbMATHGoogle Scholar
  16. 16.
    Na, K.S., Kim, J.H.: Thermal postbuckling investigation of functionally graded plates using 3-D finite element method. Finite Elem. Des. Anal. 42, 748–756 (2006)CrossRefGoogle Scholar
  17. 17.
    Wu, T.-L., Shukla, K.K., Huang, J.H.: Post-buckling analysis of functionally graded rectangular plates. Compos. Struct. 81, 1–10 (2007)CrossRefGoogle Scholar
  18. 18.
    Lal, A., Jagtap, K.R., Singh, B.N.: Post buckling response of functionally graded materials plate subjected to mechanical and thermal loadings with random material properties. Appl. Math. Model. 37, 2900–2920 (2013)MathSciNetCrossRefzbMATHGoogle 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.
    Taczała, M., Buczkowski, R., Kleiber, M.: Nonlinear buckling and post-buckling response of stiffened FGM plates in thermal environments. Compos. Part B 109, 238–247 (2017)CrossRefGoogle Scholar
  21. 21.
    Liew, K.M., Zhao, X., Ferreira, A.J.M.: A review of meshless methods for laminated and functionally graded plates and shells. Compos. Struct. 93, 2031–2041 (2011)CrossRefGoogle Scholar
  22. 22.
    Lee, Y.Y., Zhao, X., Reddy, J.N.: Postbuckling analysis of functionally graded plates subject to compressive and thermal loads. Comput. Methods Appl. Mech. Eng. 199, 1645–1653 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Zhang, L.W., Liew, K.M., Reddy, J.N.: Postbuckling behavior of bi-axially compressed arbitrarily straight-sided quadrilateral functionally graded material plates. Comput. Methods Appl. Mech. Eng. 300, 593–610 (2016)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Reddy, J.N.: Analysis of functionally graded plates. Int. J. Numer. Methods Eng. 47, 663–684 (2000)CrossRefzbMATHGoogle Scholar
  25. 25.
    Arya, H., Shimpi, R.P., Naik, N.K.: A zigzag model for laminated composite beams. Compos. Struct. 56, 21–24 (2002)CrossRefGoogle Scholar
  26. 26.
    Touratier, M.: A refined theory for thick composite plates. Mech. Res. Commun. 15, 229–236 (1988)CrossRefzbMATHGoogle Scholar
  27. 27.
    Soldatos, K.P.: A transverse shear deformation theory for homogeneous monoclinic plates. Acta Mech. 94, 195–220 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Wang, J.G., Liu, G.R.: A point interpolation meshless method based on radial basis functions. Int. J. Numer. Methods Eng. 54, 1623–1648 (2002)CrossRefzbMATHGoogle Scholar
  29. 29.
    Hardy, R.L.: Theory and applications of the multiquadrics-Biharmonic method (20 years of discovery 1968–1988). Comput. Math. Appl. 19, 127–161 (1990)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Wang, J.G., Liu, G.R.: On the optimal shape parameters of radial basis functions used for 2-D meshless methods. Comput. Methods Appl. Mech. Eng. 191, 2611–2630 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Wendland, H.: Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv. Comput. Math. 4, 389–396 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Sharma, K., Kumar, D.: Nonlinear stability analysis of a perforated FGM plate under thermal load. Mech. Adv. Mater. Struct. 25, 100–114 (2018)CrossRefGoogle Scholar
  33. 33.
    Auricchio, F., Beirao da Veiga, L., Buffa, A., Lovadina, C., Reali, A., Sangalli, G.: A fully locking-free isogeometric approach for plane linear elasticity problems: a stream function formulation. Comput. Methods Appl. Mech. Eng. 197, 160–172 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Vel, S.S., Batra, R.C.: Exact solution for thermoelastic deformations of functionally graded thick rectangular plates. AIAA J. 40, 1421–1433 (2002)CrossRefGoogle Scholar
  35. 35.
    Mahi, A., Bedia, E.A.A., Tounsi, A.: 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 (2015)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Wu, C.P., Chiu, K.H., Wang, Y.M.: RMVT-based meshless collocation and element-free Galerkin methods for the quasi-3D analysis of multilayered composite and FGM plates. Compos. Struct. 93, 923–943 (2011)CrossRefGoogle Scholar
  37. 37.
    Zhao, X., Liew, K.M.: Geometrically nonlinear analysis of functionally graded plates using the element-free kp-Ritz method. Comput. Methods Appl. Mech. Eng. 198, 2796–2811 (2009)CrossRefzbMATHGoogle Scholar
  38. 38.
    Zhu, P., Zhang, L.W., Liew, K.M.: Geometrically nonlinear thermomechanical analysis of moderately thick functionally graded plates using a local Petrov–Galerkin approach with moving Kriging interpolation. Compos. Struct. 107, 298–314 (2014)CrossRefGoogle Scholar
  39. 39.
    Yamaki, N.: Postbuckling behaviour of rectangular plates with small initial curvature loaded in edge compression. ASME Trans. J. Appl. Mech. 26, 407–414 (1959)MathSciNetzbMATHGoogle Scholar
  40. 40.
    Yamaki, N.: Experiments on the postbuckling behavior of square plates loaded in edge compression. ASME Trans. J. Appl. Mech. 28, 238–244 (1961)CrossRefGoogle Scholar
  41. 41.
    Dawe, D.J., Wang, S., Lam, S.S.E.: Finite strip analysis of imperfect laminated plates under end shortening and normal pressure. Int. J. Numer. Methods Eng. 38, 4193–4205 (1995)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Vuong Nguyen Van Do
    • 1
  • Kyong-Ho Chang
    • 2
  • Chin-Hyung Lee
    • 3
    Email author
  1. 1.Applied Computational Civil and Structural Engineering Research Group, Faculty of Civil EngineeringTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Department of Civil and Environmental and Plant EngineeringChung-Ang UniversitySeoulRepublic of Korea
  3. 3.The Graduate School of Construction EngineeringChung-Ang UniversitySeoulRepublic of Korea

Personalised recommendations