Geometrically nonlinear thermomechanical analysis of moderately thick functionally graded plates using a local Petrov-Galerkin approach with moving Kriging interpolation

Composite Structures

Volumn 107, Issue 1, 2014, Pages 298-314

  Zhu, Ping ^a   Zhang, L W ^b   Liew, K M ^c  

^a HUNAN UNIVERSITY   (China)

^b SHANGHAI OCEAN UNIVERSITY   (China)

^c CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Functionally graded plates; Geometrically nonlinear analysis; Kriging interpolation; Meshless local Petrov Galerkin (MLPG); Temperature dependent thermal conductivity; Von K rm n strains

Indexed keywords

FUNCTIONALLY GRADED PLATES; GEOMETRICALLY NON-LINEAR ANALYSIS; KRIGING INTERPOLATION; MESHLESS LOCAL PETROV-GALERKIN; TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY;

DELTA FUNCTIONS; FUNCTIONALLY GRADED MATERIALS; HEAT FLUX; INTERPOLATION; ITERATIVE METHODS; NONLINEAR ANALYSIS; STIFFNESS MATRIX; TAYLOR SERIES; THERMOANALYSIS;

THERMAL CONDUCTIVITY;

EID: 84889690319     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2013.08.001     Document Type: Article

References (52)

1. Yamanouchi M, Koizumi M, Hirai T, Shiota I. Proceedings of the first international symposium on functionally gradient materials. Japan; 1990.
2. Koizumi M. Concept of FGM. Ceram Trans 1993, 34:3-10.
3. Praveen G.N., Reddy J.N. Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates. Int J Solids Struct 1998, 35:4457-4476.
4. Reddy J.N. Analysis of functionally graded plates. Int J Numer Meth Eng 2000, 47:663-684.
5. Jha D.K., Kant T., Singh R.K. A critical review of recent research on functionally graded plates. Compos Struct 2013, 96:833-849.
6. Shen H.S. Nonlinear bending response of functionally graded plates subjected to transverse loads and in thermal environments. Int J Mech Sci 2002, 44:561-584.
7. Na K.S., Kim J.H. Nonlinear bending response of functionally graded plates under thermal loads. J Therm Stresses 2006, 29:245-261.
8. Ma L.S., Wang T.J. Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings. Int J Solids Struct 2003, 40:3311-3330.
9. Yang J., Kitipornchai S., Liew K.M. Large amplitude vibration of thermo-electro-mechanically stressed FGM laminated plates. Comput Meth Appl Mech Eng 2003, 192:3861-3885.
10. Zhao X., Liew K.M. Geometrically nonlinear analysis of functionally graded plates using the element-free kp-Ritz method. Comput Meth Appl Mech Eng 2009, 198:2796-2811.
11. Zhao X., Liew K.M. Geometrically nonlinear analysis of functionally graded shells. Int J Mech Sci 2009, 51:131-144.
12. Sepahi O., Forouzan M.R., Malekzadeh P. Large deflection analysis of thermo-mechanical loaded annular FGM plates on nonlinear elastic foundation via DQM. Compos Struct 2010, 92:2369-2378.
13. Talha M., Singh B.N. Large amplitude free flexural vibration analysis of shear deformable FGM plates using nonlinear finite element method. Finite Elem Anal Des 2011, 47:394-401.
14. Zhao X., Lee Y.Y., Liew K.M. Free vibration analysis of functionally graded plates using the element-free kp-Ritz method. J Sound Vib 2009, 319:918-939.
15. Zhao X., Liew K.M. Free vibration analysis of functionally graded conical shell panels by a meshless method. Compos Struct 2011, 93:649-664.
16. Zhao X., Lee Y.Y., Liew K.M. Mechanical and thermal buckling analysis of functionally graded plates. Compos Struct 2009, 90:161-171.
17. Zhao X., Liew K.M. A mesh-free method for analysis of the thermal and mechanical buckling of functionally graded cylindrical shell panels. Comput Mech 2010, 45:297-310.
18. Dai K.Y., Liu G.R., Han X., Lim K.M. Thermomechanical analysis of functionally graded material (FGM) plates using element-free Galerkin method. Comput Struct 2005, 83:1487-1502.
19. Ching H.K., Yen S.C. Meshless local Petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads. Compos Part B - Eng 2005, 36:223-240.
20. 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 and a meshless method. Compos Struct 2005, 69:449-457.
21. Liew K.M., Zhao X., Ferreira A.J.M. A review of meshless methods for laminated and functionally graded plates and shells. Compos Struct 2011, 93:2031-2041.
22. Liew K.M., Ng T.Y., Wu Y.C. Meshfree method for large deformation analysis - a reproducing kernel particle approach. Eng Struct 2002, 24:543-551.
23. Liew K.M., Wang J., Tan M.J., Rajendran S. Nonlinear analysis of laminated composite plates using the mesh-free kp-Ritz method based on FSDT. Comput Meth Appl Mech Eng 2004, 193:4763-4779.
24. Liew K.M., Peng L.X., Kitipornchai S. Geometric non-linear analysis of folded plate structures by the spline strip kernel particle method. Int J Numer Meth Eng 2007, 71:1102-1133.
25. Liew K.M., Peng L.X., Kitipornchai S. Nonlinear analysis of corrugated plates using a FSDT and a meshfree method. Comput Meth Appl Mech Eng 2007, 196:2358-2376.
26. Zhu P., Liew K.M. Free vibration analysis of moderately thick functionally graded plates by local Kriging meshless method. Compos Struct 2011, 93:2925-2944.
27. Bui T.Q., Nguyen M.N., Zhang C., Pham D.A.K. An efficient meshfree method for analysis of two-dimensional piezoelectric structures. Smart Mater Struct 2011, 20:065016.
28. Bui T.Q., Nguyen M.N., Zhang C. Buckling analysis of Reissner-Mindlin plates subjected to in-plane edge loads using a shear-locking-free and meshfree method. Eng Anal Bound Elem 2011, 35:1038-1053.
29. Bui T.Q., Nguyen M.N., Zhang C.Z. An efficient meshfree method for vibration analysis of laminated composite plates. Comput Mech 2011, 1-19.
30. Dai B.D., Cheng Y.M. An improved local boundary integral equation method for two-dimensional potential problems. Int J Appl Mech 2010, 2:421-436.
31. Zheng B.J., Dai B.D. Improved meshless local Petrov-Galerkin method for two-dimensional potential problems. Acta Phys Sin-Ch Ed 2010, 59:5182-5189.
32. Yang X.L., Dai B.D., Li Z.F. Meshless local Petrov-Galerkin method with complex variables for elasticity. Acta Phys Sin-Ch Ed 2012, 61:050204.
33. Yang X.L., Dai B.D., Zhang W.W. The complex variable meshless local Petrov-Galerkin method of solving two-dimensional potential problems. Chinese Phys B 2012, 21:100208.
34. Dai B.D., Cheng J., Zheng B.J. A moving Kriging interpolation-based meshless local Petrov-Galerkin method for elastodynamic analysis. Int J Appl Mech 2013, 5:1350011.
35. Zheng B.J., Dai B.D. A meshless local moving Kriging method for two-dimensional solids. Appl Math Comput 2011, 218:563-573.
36. Li X.G., Dai B.D., Wang L.H., et al. A moving Kriging interpolation-based boundary node method for two-dimensional potential problems. Chinese Phys B 2010, 19:120202.
37. Gu Y.T., Wang Q.X., Lam K.Y. A meshless local Kriging method for large deformation analyses. Comput Meth Appl Mech Eng 2007, 196:1673-1684.
38. Huang X.L., Shen H.S. Nonlinear vibration and dynamic response of functionally graded plates in thermal environments. Int J Solids Struct 2004, 41:2403-2427.
39. Kim Y.W. Temperature dependent vibration analysis of functionally graded rectangular plates. J Sound Vib 2005, 284:531-549.
40. Olea R. Geostatistics for engineers and earth scientists 1999, Kluwer Academic, Boston.
41. Yang J., Shen H.S. Vibration characteristics and transient response of shear-deformable functionally graded plates in thermal environments. J Sound Vib 2002, 255:579-602.
42. Reddy J.N., Chin C.D. Thermomechanical analysis of functionally graded cylinders and plates. J Therm Stresses 1998, 21:593-626.
43. Reddy J.N. Mechanics of laminated composite plates and shells: theory and analysis 2004, CRC Press, Boca Raton (FL).
44. Efraim E., Eisenberger M. Exact vibration analysis of variable thickness thick annular isotropic and FGM plates. J Sound Vib 2007, 299:720-738.
45. Bobaru F., Mukherjee S. Meshless approach to shape optimization of linear thermoelastic solids. Int J Numer Meth Eng 2002, 53:765-796.
46. Zenkour A.M., Sobhy M. Thermal buckling of functionally graded plates resting on elastic foundations using the trigonometric theory. J Therm Stresses 2011, 34:1119-1138.
47. Javaheri R., Eslami M.R. Thermal buckling of functionally graded plates based on higher order theory. J Therm Stresses 2002, 25:603-625.
48. Liew K.M., Wang J., Tan M.J., Rajendran S. Postbuckling analysis of laminated composite plates using the mesh-free kp-Ritz method. Comput Meth Appl Mech Eng 2006, 195:551-570.
49. Hegen D. Element-free Galerkin methods in combination with finite element approaches. Comput Meth Appl Mech Eng 1996, 135:143-166.
50. Atluri S.N., Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput Mech 1998, 22:117-127.
51. Liu G.R. Meshfree methods: moving beyond the finite element method 2010, CRC Press. 2nd ed.
52. Mercier B. Lectures on topics in finite element solution of elliptic problems 1979, Springer-Verlag, Heidelberg.