Main Article Content

Abstract

Nonlinear behavior of Functionally Graded Material (FGM) skew plates under in-plane load is investigated here using a shear deformable eight noded iso-parametric plate bending finite element. The material is graded in the thickness direction according to a power-law distribution in terms of volume fractions of the constituents. The effective material properties are estimated using Mori-Tanaka homogenization method. The nonlinear governing equations for the FGM plate under in-plane load are solved by Newton-Raphson technique to obtain the out-of-plane central deflection and in-plane displacement of the loaded edge. The existence of bifurcation-type of buckling for FGM plates is examined for different boundary conditions, constituent gradient index, and skew angle.

Keywords

FGM plate, Volume fraction index, in-plane load, Extension-bending coupling, Bifurcation buckling, Secondary instability, Finite element.

Article Details

How to Cite
Prakash, T., Singha, M., & Ganapathi, M. (2023). Nonlinear Behavior of Fgm Skew Plates Under In-Plane Load. Journal of Aerospace Sciences and Technologies, 61(2), 325–333. https://doi.org/10.61653/joast.v61i2.2009.527

References

  1. Koizumi M., "The Concept of FGM", Ceramic Transaction: Functionally Graded Material. 1993, 34, pp. 3-10.
  2. Suresh S. and Mortensen A., "Functionally Graded Metals and Metal-ceramic Composites Part 2. Thermomechanical Behavior" Int. Mat. Rev. 1997, 42, pp. 85-116.
  3. Birman V., "Buckling of Functionally Graded Hybrid Composite Plates", Proceedings of the 10th Conference on Engineering Mechanics, Boulder, Colorado, 1995, 2, pp.1199-1202.
  4. Feldman E. and Aboudi J., "Buckling Analysis of Functionally Graded Plates Subjected to Uniaxial Loading", Composite Structures, 1997, 38, pp. 29- 36.
  5. Javaheri R. and Eslami M. R.,"Buckling of Functionally Graded Plates Under in-plane Compressive Loading", ZAMM, 2002, 82, pp.277-283.
  6. Chen X. L. and Liew K. M., "Buckling of Rectangular Functionally Graded Material Plates Subjected to Nonlinearly Distributed In-plane Edge Loads", Smart Materials and Structures, 2004, 3, pp.1430- 1437.
  7. Ganapathi M., Prakash T. and Sundararajan N., "Influence of Functionally Graded Material on Buckling of Skew Plates under Mechanical Loads", Journal of Engineering Mechanics, ASCE, 2006, 132 (8), pp.902-905.
  8. Najafizadeh M. M. and Eslami, M. R., "Buckling Analysis of Circular Plates of Functionally Graded Materials Under Uniform Radial Compression", Int. J. of Mech. Sci., 2002, 44, pp.2479-2493.
  9. Sharjat B. A. S., Javaheri R. and Eslami M. R.,"Buckling of Imperfect Functionally Graded Plates Under in-plane Compressive Loading", Thin-Walled Structures, 2005, 43, pp.1020-1036.
  10. Leissa A.W., "Conditions for Laminated Plates to Remain Flat Under Inplane Loading", Composite Structures, 1986, 6, pp.261-270.
  11. Qatu M. S. and Leissa A. W., "Buckling or Transverse Deflections of Unsymmetrically Laminated Plates Subjected to In-plane Loads", AIAA Journal, 1993, 31, pp.189-194.
  12. Ayodogdu M., "Conditions for Functionally Graded Plates to Remain Flat Under In-plane Loads by Classical Plate Theory", Composite Structures, 2007 (in press).
  13. Liew K. M., Yang J. and Kitipornchai S., "Postbuckling of Piezoelectric FGM Plates Subject to Thermoelectro- mechanical Loading", Int. J. of Solids and Struct. 2003, 40, pp.3869-3892.
  14. Shen H-S., "Postbuckling of FGM Plates with Piezoelectric Actuators Under Thermo-Electro-Mechanical Loadings", Int. J. of Solids and Struct., 2005, 42, pp.6101-6121.
  15. Prathap G., Naganarayana B.P. and Somashekar B. R., "A Field Consistency Analysis of the Isoparametric Eight-noded Plate Bending Elements", Computers and Structures, 1988, 29, pp.857-874.
  16. Ganapathi M., Varadan TK. and Sarma B.S., "Nonlinear Flexural Vibrations of Laminated Orthotropic plates", Computers and Structures, 1991, 39, pp.685- 688.
  17. Cheng Z-Q. and Batra R. C., "Three Dimensional Thermoelastic Deformations of a Functionally Graded Elliptic Plate. Composites Part B", Engineering, 2000, 31, pp.97-106.
  18. Mori T. and Tanaka K., "Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions". Acta Metallurgica, 1973, 21, pp.571-574.
  19. Zienkiewicz O. C. and Taylor R. L., "The Finite Element Method", McGraw-Hill, Singapore, 1989.
  20. Hinton E. and Huang H. C., "A Family of Quadrilateral Mindlin Plate Elements with Substitute Shear Strain Fields", Computers and Structures, 1986, 23, pp. 409-431.
  21. Singha M. K., Ramachandra L. S. and Bandyopadhyay J. N., "Thermal Postbuckling Analysis of Laminated Composite Plates", Composite Structures, 2001, 54, pp.453-458.
  22. Wang S., "Buckling Analysis of Skew Fibre-reinforced Composite Laminates Based on First-order shear Deformation Theory", Composite Structures, 1997, 37, pp.5-19.
  23. Sundaresan P., Singh G. and Rao G. V., "Buckling and Post-buckling Analysis of Moderately Thick Laminated Rectangular Plates", Computers and Structures, 1996, 61, pp.79-86.

Most read articles by the same author(s)