Buckling and post-buckling analysis of FGM plates resting on the two-parameter Vlasov foundation using general third-order plate theory

Downloads

Authors

  • M. Taczała West Pomeranian University of Technology in Szczecin, Faculty of Maritime Technology and Transport, Poland
  • R. Buczkowski West Pomeranian University of Technology in Szczecin, Faculty of Maritime Technology and Transport, Poland
  • M. Kleiber Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland

Abstract

We present a nonlinear finite element analysis to investigate the buckling and post-buckling behaviour of functionally graded material (FGM) plates resting on the elastic foundation. The material properties are assumed to vary gradually across the thickness according to a power law distribution. The starting point of the investigation is the generalized third-order plate theory and the Vlasov model of elastic foundation having properties varying throughout the depth. The plates are subjected to bending to verify the formulation and compression loads including buckling and post-buckling analysis to investigate the influence of various parameters on the structural response.

Keywords:

FGM plate, elastic foundation, post-buckling, nonlinear finite element analysis

References


  1. K. Swaminathan, D.T. Naveenkumar, A.M. Zenkour, E. Carrera, Stress, vibration and buckling analyses of FGM plates – A state-of-the-art review, Composite Structures, 120, 10–31, 2015, https://doi.org/10.1016/j.compstruct.2014.09.070.

  2. K. Swaminathan, D.M. Sangeetha, Thermal analysis of FGM plates – A critical review of various modeling techniques and solution methods, Composite Structures, 160, 43–60, 2017, https://doi.org/10.1016/j.compstruct.2016.10.047.

  3. A. Hassan Ahmed Hassan, N. Kurgan, A Review on buckling analysis of functionally graded plates under thermo-mechanical loads, International Journal of Engineering and Applied Sciences, 11, 1, 345–368, 2019, https://doi.org/10.24107/ijeas.555719.

  4. K. Swaminathan, D.T. Naveenkumar, Higher order refined computational models for the stability analysis of FGM plates – Analytical solutions, European Journal of Mechanics – A/Solids, 47, 349–361, 2014, https://doi.org/10.1016/j.euromechsol.2014.06.003.

  5. R. Javaheri, M.R. Eslami, Buckling of functionally graded plates under in-plane compressive loading, ZAMM-Zeitschrift für Angewandte Mathematik und Mechanik, 82, 4, 277–283, 2002, https://doi.org/10.1002/1521-4001(200204)82:4%3C277::AID-ZAMM277%3E3.0.CO%3B2-Y.

  6. B.A. Samsam-Shariat, M.R. Eslami, Buckling of thick functionally graded plates under mechanical and thermal loads, Composite Structures, 78, 3, 433–439, 2007, https://doi.org/10.1016/j.compstruct.2005.11.001.

  7. T. Prakash, M.K. Singha, M. Ganapathi, Thermal postbuckling analysis of FGM skew plates, Engineering Structures, 30, 1, 22–32, 2008, https://doi.org/10.1016/j.engstruct.2007.02.012.

  8. T. Prakash, M. Singha, M. Ganapathi, Influence of neutral surface position on the nonlinear stability behavior of functionally graded plates, Computational Mechanics, 43, 3, 341–350, 2009, https://doi.org/10.1007/s00466-008-0309-8.

  9. M. Aydogdu, Conditions for functionally graded plates to remain flat under inplane loads by classical plate theory, Composite Structures, 82, 1, 155–7, 2008, https://doi.org/10.1016/j.compstruct.2006.10.004.

  10. Y.Y. Lee, X. Zhao, J.N. Reddy, Post-buckling analysis of functionally graded plates subjected to compressive and thermal loads, Computer Methods in Applied Mechanics and Engineering, 199, 25-28, 1645–1653, 2010, https://doi.org/10.1016/j.cma.2010.01.008.

  11. A.M. Zenkour, M. Sobhy, Thermal buckling of various types of FGM sandwich plates, Composite Structures, 93, 1, 93–102, 2018, https://doi.org/10.1016/j.compstruct.2010.06.012.

  12. N.D. Duc, H. Van Tung, Mechanical and thermal postbuckling of higher order shear deformable functionally graded plates on elastic foundations, Composite Structures, 93, 11, 2874–2881, 2011, https://doi.org/10.1016/j.compstruct.2011.05.017.

  13. M. Bodaghi, A.R. Saidi, Stability analysis of functionally graded rectangular plates under nonlinearly varying in-plane loading resting on elastic foundation, Archive of Applied Mechanics, 81, 6, 765–780, 2011, https://doi.org/10.1007/s00419-010-0449-0.

  14. A.H. Akbarzadeh, M. Abbasi, M.R. Eslami, Coupled thermo-elasticity of functionally graded plates based on the third-order shear deformation theory, Thin-Walled Structures, 53, 141–155, 2012, https://doi.org/10.1016/j.tws.2012.01.009.

  15. K. Kowal-Michalska, R. Mania, Static and dynamic thermo-mechanical buckling loads of functionally graded plates, Mechanics and Mechanical Engineering, 17, 1, 99–112, 2013.

  16. D.G. Zhang, Modeling and analysis of FGM rectangular plates based on physical neutral surface and high order shear deformation theory, International Journal of Mechanical Sciences, 68, 92–104, 2013, https://doi.org/10.1016/j.ijmecsci.2013.01.002.

  17. M. Latifi, F. Farhatnia, M. Kadkhodaei, Buckling analysis of rectangular functionally graded plates under various edge conditions using Fourier series expansion, European Journal of Mechanics – A/Solids, 41, 16–27, 2013, https://doi.org/10.1016/j.euromechsol.2013.01.008.

  18. H.T. Thai, B. Uy, Levy solution for buckling analysis of functionally graded plates based on a refined plate theory, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 12, 2649–2664, 2013, https://doi.org/10.1177/0954406213478526.

  19. M.H. Mansouri, M. Shariyat, Biaxial thermo-mechanical buckling of orthotropic auxetic FGM plates with temperature and moisture dependent material properties on elastic foundations, Composites Part B: Engineering, 83, 88–104, 2015, https://doi.org/10.1016/j.compositesb.2015.08.030.

  20. S.-C. Han, W.-T. Park, W.-Y. Jung, Four-variable refined plate theory for dynamic stability analysis of S-FGM plates based on physical neutral surface, Composite Structures, 131, 1081–1089, 2015, https://doi.org/10.1016/j.ijmecsci.2016.03.001.

  21. Y-H. Lee, S-I. Bae, J-H. Kim, Thermal buckling behavior of functionally graded plates based on neutral surface, Composite Structures, 137, 208–214, 2016, https://doi.org/10.1016/j.compstruct.2015.11.023.

  22. Y. Fan, H. Wang, Nonlinear bending and postbuckling analysis of matrix cracked hybrid laminated plates containing carbon nanotube reinforced composite layers in thermal environments, Composites Part B: Engineering, 86, 1–16, 2016, https://doi.org/10.1016/j.compositesb.2015.09.048.

  23. A. Chikh, A. Bakora, H. Heireche, M.S.A. Houari, A. Tounsi, E.A. Adda Bedia, Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory, Structural Engineering and Mechanics, 57, 4, 617–639, 2016, https://doi.org/10.12989/sem.2016.57.4.617.

  24. S. Shams, B. Soltani, M. Memar Ardestani, The effect of elastic foundations on the buckling behavior of functionally graded carbon nanotube-reinforced composite plates in thermal environments using a meshfree method, Journal of Solid Mechanics, 8, 2, 262–279, 2016.

  25. Y. Yu, H.S. Shen, H. Wang, D. Hui, Postbuckling of sandwich plates with graphene-reinforced composite face sheets in thermal environments, Composites Part B: Engineering, 135, 72–83, 2018, https://doi.org/10.1016/j.compositesb.2017.09.045.

  26. P.H. Cong, T.M. Chien, N.D. Khoa, N.D. Duc, Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy’s HSDT, Aerospace Science and Technology, 77, 419–428, 2018, https://doi.org/10.1016/j.ast.2018.03.020.

  27. M.G. Shahrestani, M. Azhari, H. Foroughi, Elastic and inelastic buckling of square and skew FGM plates with cutout resting on elastic foundation using isoparametric spline finite strip method, Acta Mechanica, 229, 2079–2096, 2018, https://doi.org/10.1007/s00707-017-2082-2.

  28. A. Gupta, M. Talha, Static and Stability Characteristics of Geometrically Imperfect FGM Plates Resting on Pasternak Elastic Foundation with Microstructural Defect, The Arabian Journal for Science and Engineering, 43, 4931–4947, 2018, https://doi.org/10.1007/s13369-018-3240-0.

  29. J.S. Moita, A.L. Araújo, V.F. Correia, C.M.M. Soares, Buckling and nonlinear response of functionally graded plates under thermo-mechanical loading, Composite Structures, 202, 719–730, 2018, https://doi.org/10.1016/j.compstruct.2018.03.082.

  30. J.S. Moita, A.L. Araújo, V.F. Correia, C.M.M. Soares, Buckling behavior of composite and functionally graded material plates, European Journal of Mechanics A/Solids, 80, 103921, 2020, https://doi.org/10.1016/j.euromechsol.2019.103921.

  31. V.N.V. Do, C.H. Lee, A new nth-order shear deformation theory for isogeometric thermal buckling analysis of FGM plates with temperature-dependent material properties, Acta Mechanica, 230, 3783–3805, 2019, https://doi.org/10.1007/s00707-019-02480-1.

  32. M. Sobhy, A.M. Zenkour, Porosity and inhomogeneity effects on the buckling and vibration of double-FGM nanoplates via a quasi-3D refined theory, Composite Structures, 220, 289–303, 2019, https://doi.org/10.1016/j.compstruct.2019.03.096.

  33. S.J. Singh, S.P. Harsha, Buckling analysis of FGM plates under uniform, linear and non-linear in-plane loading, Journal of Mechanical Science and Technology, 33, 4, 1761–1767, 2019, https://doi.org/10.1007/s12206-019-0328-8.

  34. V.N.V. Do, K.H. Chang, C.H. Lee, Post-buckling analysis of FGM plates under in-plane mechanical compressive loading by using a mesh-free approximation, Archive of Applied Mechanics, 89, 1421–1446, 2019, https://doi.org/10.1007/s00419-019-01512-5.

  35. Y. Liu, S. Su, H. Huang, Y. Liang, Thermal-mechanical coupling buckling analysis of porous functionally graded sandwich beams based on physical neutral plane, Composites Part B-Engineering, 168, 236–242, 2019, https://doi.org/10.1016/j.compositesb.2018.12.063.

  36. A.M. Zenkour, A.F. Radwan, Bending and buckling analysis of FGM plates resting on elastic foundations in hygrothermal environment, Archives of Civil and Mechanical Engineering, 20, 4, 198–220, 2020, https://doi.org/10.1007/s43452-020-00116-z.

  37. M. Taczała, R. Buczkowski, M. Kleiber, Nonlinear free vibration of pre- and post-buckled FGM plates on two-parameter foundation in the thermal environment, Composite Structures, 137, 85–92, 2016, https://doi.org/10.1016/j.compstruct.2015.11.017.

  38. M. Taczała, R. Buczkowski, M. Kleiber, Nonlinear buckling and post-buckling response of stiffened FGM plates in thermal environments, Composites Part B: Engineering, 109, 238–247, 2017, https://doi.org/10.1016/j.compositesb.2016.09.023.

  39. M. Taczała, R. Buczkowski, M. Kleiber, Elastic-plastic buckling and postbuckling finite element analysis of plates using higher-order theory, International Journal of Structural Stability and Dynamics, 21, 7, 2150095, 2021, https://doi.org/10.1142/S0219455421500954.

  40. J.N. Reddy, J. Kim, A nonlinear modified couple stress-based third-order theory of functionally graded plates, Composite Structures, 94, 1128–1143, 2012, https://doi.org/10.1590/S1679-78252014000300006.

  41. M. Taczała, R. Buczkowski, M. Kleiber, Analysis of FGM plates based on physical neutral surface using general third-order plate theory, Composite Structures, 301, 1–7, 2022, https://doi.org/10.1016/j.compstruct.2022.116218.

  42. C.V.G. Vallabhan, A.T. Daloglu, Consistent FEM-Vlasov model for plates on layered soil, Journal of Structural Engineering – ASCE, 125, 10, 108–113, 1999, https://doi.org/10.1061/(ASCE)0733-9445(1999)125:1(108).

  43. B.N. Pandya, T. Kant, A simple finite element formulation of a higher-order theory for unsymmetrically laminated composite plates, Composite Structures, 9, 3, 215–246, 1988, https://doi.org/10.1016/0263-8223(88)90015-3.

  44. J. Kim, J.N. Reddy, A general third-order theory of functionally graded plates with modified couple stress effect and the von Kármán nonlinearity: theory and finite element analysis, Acta Mechanica, 226, 2973–2998, 2015, https://doi.org/10.1007/s00707-015-1370-y.

  45. E. Carrera, Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking, Archives of Computational Methods in Engineering, 10, 215–296, 2003, https://doi.org/10.1007/BF02736224.

  46. A.M.A. Neves, A.J.M. Ferreira, E. Carrera, M. Cinefra, C.M.C. Roque, R.M.N. Jorge, C.M.M. Soares, Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique, Composites Part B: Engineering, 44, 1, 657–674, 2013, https://doi.org/10.1016/j.compositesb.2012.01.089.

  47. S-H. Chi, Y-L. Chung, Mechanical behavior of functionally graded material plates under transverse load Part II: numerical results, International Journal of Solids and Structures, 43, 13, 3675–3691, 2006, https://doi.org/10.1016/j.ijsolstr.2005.04.010.

  48. M.M. Filonenko-Borodich, Some approximate theories of elastic foundation. Uchenyie Zapiski Moskovskogo Gosudarstvennogo Universiteta, Mekhanika, 46, 3–18, 1940 [in Russian].

  49. P.L. Pasternak, New Method of Calculation for Flexible Substructures on Two-parameter Elastic Foundation, Gosudarstvennoe Izdatelstvo Literatury po Stroitelstvu i Architekture, Moscow, pp. 1–56, 1954 [in Russian].

  50. V.Z. Vlasov, N.N. Leontiev, Beams, Plates and Shells on Elastic Foundations, GIFML, Moskau, 1960, [in Russian] or translated from Russian by Foundation: Israel Program for Scientific Translations, Jerusalem, 1966.

  51. M. Celik, M. Omurtag, Determination of the Vlasov foundation parameters-quadratic variation of elasticity modulus using FE analysis, Structural Engineering and Mechanics, 19, 6, 619–637, 2005, https://doi.org/10.12989/sem.2005.19.6.619.

  52. C.V.G. Vallabhan, W.T. Straughan, Y.C. Das, Refined model for analysis of plates on elastic foundations, Journal of Engineering Mechanics – ASCE, 117, 12, 2830–2844, 1991, https://doi.org/10.1061/(ASCE)0733-9399(1991)117:12(2830).

  53. M. Çelik, A. Saygun, A method for the analysis of plates on a two-parameter foundation, International Journal of Solids and Structures, 36, 19, 2891–2915, 1999, https://doi.org/10.1016/S0020-7683(98)00135-8.

  54. R. Buczkowski, W. Torbacki, Finite element modelling of thick plates on two-parameter elastic foundation, International Journal of Numerical and Analytical Methods in Geomechanics, 25, 14, 1409–1427, 2001, https://doi.org/10.1002/nag.187.

  55. R. Buczkowski, M. Taczała, M. Kleiber, A 16-node locking-free Mindlin plate resting on two-parameter elastic foundation – static and eigenvalue analysis, Computer Assisted Methods in Engineering and Science, 22, 2, 99–114, 2015.

Other articles by the same author(s)