Bending analysis of thick exponentially graded plates using a new trigonometric higher order shear deformation theory

Composite Structures

Volumn 94, Issue 6, 2012, Pages 1991-2000

  Mantari, J L ^a   Guedes Soares, C ^a  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

Analytical solution; Exponentially graded plates; Higher order theory; Static analysis

Indexed keywords

3D ELASTICITY; ANALYTICAL SOLUTIONS; BENDING ANALYSIS; EXPONENTIALLY GRADED PLATES; GOVERNING EQUATIONS; HIGHER ORDER SHEAR DEFORMATION THEORY; HIGHER-ORDER THEORY; IN-PLANE DISPLACEMENT; MATERIAL VARIATION; PLATE THICKNESS; PRINCIPLE OF VIRTUAL WORK; SIMPLY SUPPORTED; THICKNESS DIRECTION; THIN PLATE; TRIGONOMETRIC SHEAR DEFORMATION THEORY;

BOUNDARY CONDITIONS; ELASTICITY; STATIC ANALYSIS;

SHEAR DEFORMATION;

EID: 84859492615     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2012.01.005     Document Type: Article

References (43)

1. Koizumi M. The concept of FGM. Ceram Trans, Funct Grad Mater 1993, 34:3-10.
2. Vel S.S., Batra R.C. Three-dimensional exact solution for the vibration of functionally graded rectangular plates. J Sound Vib 2004, 272:703-730.
3. Birman V., Byrd L.W. Modeling and analysis of functionally graded materials and structures. ASME Appl Mech Rev 2007, 60:195-216.
4. Reddy J.N. Analysis of functionally graded plates. Int J Numer Meth Eng 2000, 47:663-684.
5. Cheng Z.Q., Batra R.C. Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories. Arch Mech 2000, 52:143-158.
6. Vel S.S., Batra R.C. Three-dimensional analysis of transient thermal stresses in functionally graded plates. Int J Solids Struct 2002, 40:7181-7196.
7. Pan E. Exact solution for functionally graded anisotropic elastic composite laminates. J Compos Mater 2003, 37:1903-1920.
8. Pagano N.J. Exact solutions for rectangular bidirectional composites and sandwich plates. J Compos Mater 1969, 4:20-34.
9. Pagano N.J. Exact solutions for composite laminates in cylindrical bending. J Compos Mater 1970, 3:398-411.
10. Kashtalyan M. Three-dimensional elasticity solution for bending of functionally graded plates. Eur J Mech A/Solid 2004, 23:853-864.
11. Kashtalyan M., Menshykova M. Three-dimensional elasticity solution for sandwich panels with a functionally graded core. Compos Struct 2008, 87:36-43.
12. Qian L.F., Batra R.C., Chen L.M. Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local Petrov-Galerkin method. Composites: Part B 2004, 35:685-697.
13. Batra R.C., Jin J. Natural frequencies of a functionally graded anisotropic rectangular plate. J Sound Vib 2005, 282:509-516.
14. Ferreira A.J.M., Batra R.C., Roque C.M.C., Qian L.F., Martins P.A.L.S. Static analysis of functionally graded plates using third-order shear deformation theory. Compos Struct 2005, 69:449-457.
15. Elishakoff I. Three-dimensional analysis of an all-round clamped plate made of functionally graded materials. Acta Mech 2005, 180:21-36.
16. Zenkour A.M. Generalized shear deformation theory for bending analysis of functionally graded plates. Appl Math Model 2006, 30:67-84.
17. Ramirez F., Heyliger P.R., Pan E. Static analysis of functionally graded elastic anisotropic plates using a discrete layer approach. Composites: Part B 2006, 37:10-20.
18. Chi S.H., Chung Y.L. Mechanical behavior of functionally graded material plates under transverse load. Part I: analysis. Int J Solids Struct 2006, 43:3657-3674.
19. Chi S.H., Chung Y.L. Mechanical behavior of functionally graded material plates under transverse load. Part II: numerical results. Int J Solids Struct 2006, 43:3675-3691.
20. Zenkour A.M. Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate. Appl Math Model 2007, 77:197-214.
21. Sladek J., Sladek V., Hellmich C.H., Eberhardsteiner J. Analysis of thick functionally graded plates by local integral equation. Commun Numer Meth Eng 2007, 23:733-754.
22. Bo Y., Hao-jiang D., Wei-qiu C. Elasticity solutions for functionally graded plates in cylindrical bending. Appl Math Mech 2008, 29(8):999-1004.
23. Matsunaga H. Stress analysis of functionally graded plates subjected to thermal and mechanical loadings. Compos Struct 2009, 87:344-357.
24. Khabbaz R.S., Manshadi B.D., Abedian A. Nonlinear analysis of fgm plates under pressure loads using the higher-order shear deformation theories. Compos Struct 2009, 89:333-344.
25. Aghdam M.M., Bigdelli K., Shahmansouri N. A semi-analytical solution for bending of moderately thick curved functionally graded panels. Mech Adv Mater Struct 2010, 17:320-327.
26. Wu C.P., Li H.Y. An RMVT-based third-order shear deformation theory of multilayered functionally graded material plates. Compos Struct 2010, 92:2591-2605.
27. Talha M., Singh B.N. Static response and free vibration analysis of fgm plates using higher order shear deformation theory. Appl Math Model 2010, 34:3991-4011.
28. Vaghefi R., Baradaran G.H., Koohkan H. Three-dimensional static analysis of thick functionally graded plates by using meshless local Petrov-Galerkin (MLPG) method. Eng Anal Bound Elem 2010, 34:564-573.
29. Wu C.P., Li H.Y. RMVT-based meshless collocation and element-free Galerkin methods for the quasi-3D analysis of multilayered composite and FGM plates. Compos Struct 2011, 93:923-943.
30. Carrera E., Brischetto S., Cinefra M., Soave M. Effects of thickness stretching in functionally graded plates and shells. Composites: Part B 2011, 42:123-133.
31. Carrera E., Brischetto S., Robaldo A. Variable kinematic model for the analysis of functionally graded material plates. AIAA J 2008, 46:194-203.
32. Brischetto S. Classical and mixed advanced models for sandwich plates embedding functionally graded cores. J Mech Mater Struct 2009, 4:13-33.
33. Brischetto S, Carrera E. Classical and mixed theories for bending analysis of functionally graded materials shells. In: Proceedings of APCOM'07 in conjunction with EPMESC XI, Kyoto, Japan.
34. Brischetto S., Carrera E. Advanced mixed theories for bending analysis of functionally graded plates. Comput Struct 2010, 88:1474-1483.
35. Mantari J.L., Oktem A.S., Guedes Soares C. A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates. Int J Solids Struct 2012, 49:43-53. 2011a.
36. Levy M. Memoire sur la theorie des plaques elastique planes. J Math Pures Appl 1877, 30:219-306.
37. Stein M. Nonlinear theory for plates and shells including the effects of transverse shearing. AIAA 1986, 24(9):1537-1544.
38. Touratier M. An efficient standard plate theory. Int J Eng Sci 1991, 29(8):901-916.
39. Oktem A.S., Chaudhuri R.A. Higher-order theory based boundary-discontinuous Fourier analysis of simply supported thick cross-ply doubly curved panels. Compos Struct 2009, 89:448-458.
40. Oktem A.S., Chaudhuri R.A. Sensitivity of the response of thick doubly curved cross-ply panels to edge clamping. Compos Struct 2009, 87:293-306.
41. Oktem A.S., Guedes Soares C. Boundary discontinuous Fourier solution for plates and doubly curved panels using a higher order theory. Composites: Part B 2011, 42:842-850.
42. Mantari JL, Oktem AS, Guedes Soares C. A new higher order shear deformation theory for sandwich and composite laminated plates. Composites: Part B, doi:10.1016/j.compositesb.2011.07.017.
43. Mantari JL., Oktem AS., Guedes Soares C. Static and dynamic analysis of laminated composite and sandwich plates and shells by using a new higher-order shear deformation theory. Compos Struct 2011, 94:37-49.