Analysis of thick functionally graded plates by using higher-order shear and normal deformable plate theory and MLPG method with radial basis functions

Composite Structures

Volumn 80, Issue 4, 2007, Pages 539-552

  Gilhooley, D F ^a,d   Batra, R C ^c   Xiao, J R ^a   McCarthy, M A ^d   Gillespie Jr , J W ^a,b  

^a UNIVERSITY OF DELAWARE   (United States)

^b UNIVERSITY OF DELAWARE   (United States)

^c State University   (United States)

^d UNIVERSITY OF LIMERICK   (Ireland)

Author keywords

Functionally graded materials; Higher order shear and normal deformable plate theory; MLPG method; Radial basis function; Thick plate

Indexed keywords

BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; GALERKIN METHODS; HOMOGENIZATION METHOD; PLATES (STRUCTURAL COMPONENTS); RADIAL BASIS FUNCTION NETWORKS; SHEAR DEFORMATION;

HIGHER-ORDER SHEAR AND NORMAL DEFORMABLE PLATE THEORY (HOSNDPT); MESHLESS LOCAL PETROV-GALERKIN (MLPG) METHOD; MULTIQUADRICS;

FUNCTIONALLY GRADED MATERIALS;

COMPOSITE; COMPUTER SIMULATION; DEFORMATION; ELASTIC PROPERTY; FINITE ELEMENT ANALYSIS; SHEAR PROPERTY; STRESS; THICKNESS;

EID: 33847648493     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2006.07.007     Document Type: Article

References (45)

1. Berger R, Kwon P, Dharan CKH. High speed centrifugal casting of metal matrix composites. In: The fifth international symposium on transport phenomena and dynamics of rotating machinery, Maui, Hawaii, May 8-11; 1994.
2. Fukui Y. Fundamental investigation of functionally gradient materials manufacturing system using centrifugal force. JSME Int J Ser III 34 (1991) 144-148
3. Choy K.-L., and Felix E. Functionally graded diamond like carbon coatings on metallic substrates. Mater Sci Eng A 278 (2000) 162-169
4. 2/NiCoCrAlY coatings. Mater Sci Eng A 277 (2000) 64-76
5. Lambros A., Narayanaswamy A., Santare M.H., and Anlas G. Manufacturing and testing of a functionally graded material. J Eng Mater Technol 121 (1999) 488-493
6. Braval E., Aghahanian K., and Luszcz S.J. Microstructure and composition of alumina/aluminum composites made by the directed oxidation of aluminum. J Am Ceram Soc 73 (1990) 2610-2614
7. 3/Al alloy composite produced by melt oxidation. J Am Ceram Soc 26 (1993) 1777-1787
8. Lo K.H., Christensen R.M., and Wu E.M. A high-order theory of plate deformation. J Appl Mech 44 (1997) 663-676
9. Phan N.D., and Reddy J.N. Analysis of laminated composite plates using a higher-order shear deformation theory. Int J Num Methods Eng 21 (1985) 2201-2219
10. Batra R.C., and Vidoli S. Higher-order piezoelectric plate theory derived from a three-dimensional variational principle. AIAA J 40 (2002) 91-104
11. Kocak S., and Hassis H. A higher order shear deformable finite element for homogeneous plates. Eng Struct 25 (2003) 131-139
12. Reddy J.N. Analysis of functionally graded plates. Int J Numer Meth Eng 47 (2000) 663-684
13. Cheng Z.Q., and Batra R.C. Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories. Arch Mech 52 (2000) 143-158
14. Cheng Z.Q., and Batra R.C. Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates. J Sound Vib 229 (2000) 879-895
15. Cheng Z.Q., and Batra R.C. Three-dimensional thermoelastic deformations of a functionally graded elliptic plate. Compos: Part B 31 (2000) 97-106
16. Loy C.T., Lam K.Y., and Reddy J.N. Vibrations of functionally graded cylindrical shells. Int J Mech Sci 41 (1999) 309-324
17. Batra R.C., Vidoli S., and Vestroni F. Plane wave solutions and modal analysis in higher order shear and normal deformable plate theories. J Sound Vib 257 (2002) 63-88
18. Batra R.C., and Aimmanee S. Vibrations of thick isotropic plates with higher order shear and normal deformable plate theories. Comput Struct 83 (2005) 934-955
19. Qian L.F., Batra R.C., and Chen L.M. Elastostatic deformations of a thick plate by using a higher-order shear and normal deformable plate theory and two meshless local Petrov-Galerkin (MLPG) methods. Comput Model Eng Sci 4 (2003) 161-176
20. Qian L.F., Batra R.C., and Chen L.M. Static and dynamic deformations of thick functionally graded elastic plate by using higher-order shear and normal deformable plate theory and meshless local Petrov-Galerkin method. Compos: Part B 35 (2004) 685-697
21. Qian L.F., and Batra R.C. Transient thermoelastic deformations of a thick functionally graded plate. J Therm Stresses 27 (2004) 705-740
22. Belytschko T., Lu Y.Y., and Gu L. Element-free Galerkin methods. Int J Num Meth Eng 37 (1994) 229-256
23. Liu W.K., Jun S., and Zhang Y. Reproducing kernel particle methods. Int J Num Meth Fluids 20 (1995) 1081-1106
24. Duarte C.A., and Oden J.T. An h-p adaptive method using clouds. Comput Meth Appl Mech Eng 139 (1996) 237-262
25. Babuska I., and Melenk J. The partition of unity method. Int J Num Meth Eng 40 (1997) 727-758
26. Atluri S.N., and Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput Mech 22 (1998) 117-127
27. Atluri S.N., and Shen S. The meshless local Petrov-Galerkin (MLPG) method (2002), Tech Science Press
28. Hardy R.L. Multiquadric equations of topography and other irregular surfaces. J Geophys Res 76 (1971) 1905-1915
29. Kansa E.J. Multiquadrics - A scattered data approximation scheme with application to computational fluid-dynamics - I and II. Comput Math Appl 19 (1990) 127-161
30. Golberg M.A., Chen C.S., and Karur S.R. Improved multiquadric approximation for partial differential equations. Eng Anal Bound Elem 18 (1996) 9-17
31. Fasshauer G.E. Solving partial differential equations by collocation with radial basis functions. In: Le M haut A., Rabut C., and Schumaker L.L. (Eds). Surface fitting and mutliresolution methods (1997), Vanderbilt University Press, Nashville TN 131-138
32. Wendland H. Meshless Galerkin method using radial basis functions. Math Comput 68 (1999) 1521-1531
33. Liu G.R., and Gu Y.T. A local radial point interpolation method (LRPIM) for free vibration analysis of 2D solids. J Sound Vib 246 (2001) 29-46
34. Wang J.G., and Liu G.R. On the optimal shape parameters of radial basis functions used for 2D meshless methods. Comput Methods Appl Mech Eng 191 (2002) 2611-2630
35. Xiao J.R., and McCarthy M.A. A local Heaviside weighted meshless method for two-dimensional solids using radial basis functions. Comput Mech 31 (2003) 301-315
36. Xiao J.R., Gama B.A., Gillespie Jr. J.W., and Kansa E.J. Meshless solutions of 2D contact problems by subdomain variational inequality and MLPG method with radial basis functions. Eng Anal Bound Elem 29 (2005) 95-106
37. Ferreira A.J.M., Batra R.C., Roque C.M.C., Qian L.F., and Martins P.A.L.S. Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method. Compos Struct 69 (2005) 449-457
38. Mori T., and Tanaka K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 21 (1973) 571-574
39. Vel S.S., and Batra R.C. Exact solution for thermoelastic deformations of functionally graded thick rectangular plates. AIAA J 40 (2002) 1421-1433
40. Frohlich H., and Sack R. Theory of the rheological properties of dispersions. Proc R Soc A185 (1946) 415-430
41. Hill R. A self-consistent mechanics of composite materials. J Mech Phys Solids 13 (1965) 213-222
42. Jiang B., and Batra R.C. Effective properties of a piezocomposite containing shape memory alloy and inert inclusions. Continuum Mech Therm 14 (2002) 87-111
43. Vel S.S., and Batra R.C. Three-dimensional thermoelastic analysis of transient thermal stresses in functionally graded plates. Int J Solids Struct 40 (2003) 7181-7196
44. Vel S.S., and Batra R.C. Three-dimensional exact solution for the vibration of functionally graded rectangular plates. J Sound Vib 272 (2004) 703-730
45. Xiao JR, Batra RC, Gilhooley DF, Gillespie Jr JW, McCarthy MA. Bending analysis of thick plates by using a higher-order shear and normal deformable plate theory and MLPG method with radial basis functions. Comput Meth Appl Mech Eng, in press.