TSDT theory for free vibration of functionally graded plates with various material properties

2021;
: pp. 691–704
https://doi.org/10.23939/mmc2021.04.691
Received: May 23, 2021
Accepted: June 07, 2021
1
Hassan II University of Casablanca, National Higher School of Arts and Crafts (ENSAM Casablanca)
2
Hassan II University of Casablanca, National Higher School of Arts and Crafts (ENSAM Casablanca)
3
Hassan II University of Casablanca, National Higher School of Arts and Crafts (ENSAM Casablanca)
4
Hassan II University of Casablanca, National Higher School of Arts and Crafts (ENSAM Casablanca)

In this work, an implicit algorithm is used for analyzing the free dynamic behavior of Functionally Graded Material (FGM) plates.  The Third order Shear Deformation Theory (TSDT) is used to develop the proposed model.  In this contribution, the formulation is written without any homogenization technique as the rule of mixture.  The Hamilton principle is used to establish the resulting equations of motion.  For spatial discretization based on Finite Element Method (FEM), a quadratic element with four and eight nodes is adopted using seven degrees of freedom per node.  An implicit algorithm is used for solving the obtained problem.  To study the accuracy and the performance of the proposed approach, we present comparisons with literature and laminate composite modeling results for vibration natural frequencies.  Otherwise, we examine the influence of the exponent of the volume fraction which reacts the plates "P-FGM" and "S-FGM".  In addition, we study the influence of the thickness on "E-FGM" plates.

  1. Vinh P. V., Dung N. T., Tho N. C., Thom D. V., Hoa L. K.  Modified single variable shear deformation plate theory for free vibration analysis of rectangular FGM plates.  Structures. 29, 1435–1444 (2021).
  2. Auada S. P., Pracianoa J. S. C., Barrosoa E. S., Sousa Jr J. B. M., Parente Juniora E.  Isogeometric Analysis of FGM Plates.  Materials Today: Proceedings. 8 (3), 738–746 (2019).
  3. Kim S. E., Duc N. D., Nam V. H., Van Sy N.  Nonlinear vibration and dynamic buckling of eccentrically oblique stiffened FGM plates resting on elastic foundations in thermal environment.  Thin-Walled Structures. 142, 287–296 (2019).
  4. Fu T., Chen Z., Yu H., Wang Z., Liu X.  An analytical study of sound transmission through corrugated core FGM sandwich plates filled with porous material.  Composites Part B: Engineering, 151, 161–172 (2018).
  5. Sharma P., Meena M., Khinchi A.  Modal study of bi direction FGM plate.  Materials Today: Proceedings. 44 (1), 1604–1608 (2021).
  6. Kar U. K., Srinivas J.  Material modeling and analysis of hydroxyapatite/titanium FGM plate under thermo-mechanical loading conditions.  Materials Today: Proceedings. 33 (8), 5498–5504 (2020).
  7. Katili I., Batoz J. L., Maknun I. J., Katili A. M.  On static and free vibration analysis of FGM plates using an efficient quadrilateral finite element based on DSPM.  Composite Structures. 261, 113514 (2021).
  8. Zheng H., Sladek J., Sladek V., Wang S. K.,  Wen P. H.  Hybrid meshless/displacement discontinuity method for FGM Reissner's plate with cracks.  Applied Mathematical Modelling. 90, 1226–1244 (2021).
  9. Hassan A. H. A., Kurgan N.  Bending analysis of thin FGM skew plate resting on Winkler elastic foundation using multi-term extended Kantorovich method.  Engineering Science and Technology, an International Journal. 23 (4), 788–800 (2020).
  10. Yang H. S., Dong C. Y.,  Wu Y. H.  Postbuckling analysis of multi-directional perforated FGM plates using NURBS-based IGA and FCM.  Applied Mathematical Modelling. 84, 466–500 (2020).
  11. Minh P. P., Manh D. T., Duc N. D.  Free vibration of cracked FGM plates with variable thickness resting on elastic foundations.  Thin-Walled Structures. 161, 107425 (2021).
  12. Li M., Yan R., Xu L., Guedes Soares C.  A general framework of higher-order shear deformation theories with a novel unified plate model for composite laminated and FGM plates.  Composite Structures. 261, 113560 (2021).
  13. Minh P. P., Duc N. D.  The effect of cracks and thermal environment on free vibration of FGM plates.  Thin-Walled Structures. 159, 107291 (2021).
  14. Tran T. T., Nguyen P. C., Pham Q. H.  Vibration analysis of FGM plate in thermal environment resting on elastic foundation using ES-MITC3 element and prediction of ANN.  Case Studies in Thermal Engineering. 24, 100852 (2021).
  15. Timesli A.  Analytical Modeling of Buckling Behavior of Porous FGM Cylindrical Shell Embedded within an Elastic Foundation.  Gazi University Journal of Science (2021).
  16. Bourihane O., Hilali Y., Mhada K.  Nonlinear dynamic response of functionally graded material plates using a high-order implicit algorithm.  Journal of Applied Mathematics and Mechanics. 100 (12), e202000087 (2020).
  17. Ghatage P. S., Kar V. R., Sudhagar P. E.  On the numerical modelling and analysis of multi-directional functionally graded composite structures: A review.  Composite Structures. 236, 111837 (2020).
  18. Huang X. L., Shen H. S.  Nonlinear vibration and dynamic response of functionally graded plates in thermal environments.  International Journal of Solids and Structures. 41 (9–10), 2403–2427 (2004).
  19. Timesli A.  Prediction of the critical buckling load of SWCNT reinforced concrete cylindrical shell embedded in an elastic foundation.  Computer and Concrete. 26 (1), 53–62 (2020).
  20. Saffah Z., Timesli A., Lahmam H., Azouani A., Amdi M.  New collocation path-following approach for the optimal shape parameter using Kernel method.  SN Applied Sciences. 3, Article number: 249 (2021).
  21. Timesli A., Braikat B., Lahmam H., Zahrouni H.  An implicit algorithm based on continuous moving least square to simulate material mixing in friction stir welding process.  Modelling and Simulation in Engineering. 2013, Article ID: 716383, 1–14 (2013).
  22. Timesli A.  Optimized radius of influence domain in meshless approach for modeling of large deformation problems.  Iranian Journal of Science and Technology-Transactions of Mechanical Engineering (2021).
  23. Mesmoudi S., Timesli A., Braikat B., Lahmam H., Zahrouni H.  A 2D mechanical-thermal coupled model to simulate material mixing observed in friction stir welding process.  Engineering with Computers. 33, 885–895 (2017).
  24. Timesli A, Braikat B., Lahmam H., Zahrouni H.  A new algorithm based on Moving Least Square method to simulate material mixing in friction stir welding.  Engineering Analysis with Boundary Elements. 50, 372–380 (2015).
  25. Belaasilia Y, Timesli A, Braikat B, Jamal M.  A numerical mesh-free model for elasto-plastic contact problems.  Engineering Analysis with Boundary Elements. 82, 68–78 (2017).
  26. El Kadmiri R., Belaasilia Y., Timesli A., Kadiri M. S.  A coupled Meshless-FEM method based on strongform of Radial Point Interpolation Method (RPIM).  Journal of Physics: Conference Series, 1743, 012039 (2021).
  27. El Kadmiri R., Belaasilia Y., Timesli A., Kadiri M. S.  Meshless approach based on MLS with additional constraints for large deformation analysis.  Journal of Physics: Conference Series. 1743, 012015 (2021).
Mathematical Modeling and Computing, Vol. 8, No. 4, pp. 691–704 (2021)