Analysis of functionally graded plates by a robust meshless method

Mechanics of Advanced Materials and Structures

Volumn 14, Issue 8, 2007, Pages 577-587

  Ferreira, A J M ^a   Roque, C M C ^a   Jorge, R M N ^a   Fasshauer, G E ^b   Batra, R C ^c  

^a UNIVERSITY OF PORTO   (Portugal)

^b ILLINOIS INSTITUTE OF TECHNOLOGY   (United States)

^c VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

Meshfree method; Radial basis functions; Shape parameter optimization; Third order shear deformation theory

Indexed keywords

BOUNDARY CONDITIONS; DEFORMATION; NUMERICAL ANALYSIS; OPTIMIZATION; PLATES (STRUCTURAL COMPONENTS); RADIAL BASIS FUNCTION NETWORKS;

BOUNDARY DISCRETIZATION; CROSS-VALIDATION TECHNIQUE; MESHFREE METHOD; ROBUST MESHLESS METHOD;

FUNCTIONALLY GRADED MATERIALS;

EID: 36649014654     PISSN: 15376494     EISSN: 15376532     Source Type: Journal    
DOI: 10.1080/15376490701672732     Document Type: Article

References (54)

1. Hardy, R. L., "Multiquadric equations of topography and other irregular surfaces," Geophys. Res. 176, 1905-1915 (1971).
2. Hardy, R. L., "Theory and applications of the multiquadric- biharmonic method: 20 years of discovery," Computers Math. Applic. 19(8/9), 163-208 (1990).
3. Kansa, E. J., "Multiquadrics- a scattered data approximation scheme with applications to computational fluid dynamics, i: Surface approximations and partial derivative estimates," Comput. Math. Appl. 19(8/9), 127-145 (1990).
4. Kansa, E. J., "Multiquadrics- a scattered data approximation scheme with applications to computational fluid dynamics, ii: Solutions to parabolic, hyperbolic and elliptic partial differential equations," Comput. Math. Appl. 19(8/9), 147-161 (1990).
5. Liu, G. R., Mesh Free Methods. CRC Press, Boca Raton, USA (2003).
6. Fasshauer, G. E., "Solving partial differential equations by collocation with radial basis functions," Surface fitting and multiresolution methods, Vol. 2 Proceedings of the 3rd International Conference on curves and surfaces 2, 131-138 (1997).
7. Powell, M. J. D., "The theory of radial, basis function approximation in 1990," In F. W. Light, editor, Advances in Numerical Analysis, pages 203240. Oxford University Press (1992).
8. Wendland, H., "Error estimates for interpolation by compactly supported radial basis functions of minimal degree," J. Approx. Theory 93, 258-296 (1998).
9. Wendland, H., Scattered Data Approximation. Cambridge University Press, Cambridge, 2005.
10. Hon, Y. C., Lu, M. W., Xue, W. M., and Zhu, Y. M., "Multiquadric method for the numerical solution of byphasic mixture model," Appl. Math Comput. 88, 153-175 (1997).
11. Hon, Y. C., Cheung, K. F., Mao, X. Z., and Kansa, E. J., "A multiquadric solution for the shallow water equation," ASCE J. Hydraulic Engineering 125(5), 524-533 (1999).
12. Wang, J. G., Liu, G. R., and Lin, P., "Numerical analysis of xbiot's consolidation process by radial point interpolation method," Int. J. Solids and Structures 39(6), 1557-1573 (2002).
13. Choy, K.-L., and Felix, E., "Functionally graded diamond-like carbon coatings on metallic substrates," Materials Science and Engineering A 278, 162-169 (2000).
14. Khor, K. A., and Gu, Y. W., "Effects of residual stress on the performance of plasma sprayed functionally graded zro2/nicocraly coatings," Materials Science and Engineering A 111, 64-76 (2000).
15. Reddy, J. N., "Analysis of functionally graded plates," International Journal for Numerical Methods in Engineering 47, 663-684 (2000).
16. Cheng, Z. Q. and Batra, R. C., "Deflection relationships between the homogeneous kirchhoff plate theory and different functionally graded plate theories," Archive of Mechanics 52, 143-158 (2000).
17. Cheng, Z. Q. and Batra, R. C., "Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates," Journal of Sound and Vibration 229, 879-895 (2000).
18. Cheng, Z. Q. and Batra, R. C., "Three-dimensional thermoelastic deformations of a functionally graded-elliptic plate," Composites: Part B 31, 97-106 (2000).
19. Loy, C. T., Reddy, J. N., and Lam, K. Y., "Vibration of functionally graded cylindrical shells," International Journal of Mechanical Sciences 41, 309-324 (1999).
20. Vel, S. S., and Batra, R. C., "Three-dimensional analysis of transient thermal stresses in functionally-graded plates," International Journal of Solids and Structures 40,7187-7196, (2004).
21. Vel, S. S., and Batra, R. C., "Three-dimensional exact solution for the vibration of functionally graded rectangular plates," Journal of Sound and Vibration 212, 703-730 (2004).
22. Jin, Z. H., and Batra, R. C., "Some basic fracture mechanics concepts in functionally graded materials," Journal of the Mechanics and Physics of Solids 44,1221-1235 (1996).
23. Jin, Z. H., and Batra, R. C., "Stress intensity relaxation at the tip of an edge crack in a functionally graded material subjected to a thermal shock," Journal of Thermal Stresses 19, 317-339 (1996).
24. Jin, Z. H., and Batra, R. C. "R-curve and strength behavior of a functionally gradient material," Material Science & Engineering, A2 42, 70-76 (1998).
25. Vel, S. S., and Batra, R. C., "Exact solution for thermoelastic deformations of functionally graded thick rectangular plates," AIAA Journal 40, 1421-1433 (2002).
26. Fedoseyev, A. I., Friedman, M. J., and Kansa, E. J., "Continuation for nonlinear elliptic partial differential equations discretized by the multiquadric method," Comput. Math. Appl. 19(8/9), 147-161 (1990).
27. Hon, Y. C., and Mao, X. Z., "On unsymmetric collocation by radial basis functions," Appl. Math. Comput. 119(2-3), 177-186 (2001).
28. Kansa, E. J., and Hon, Y. C., "Circunvecting the ill-conditioning problem with multiquadric radial basis functions," Comput. Math. Appl. 39(7-8), 123-137 (2000).
29. Belytschko, T., Krongauz, Y., Organ, D., Fleming, M., and Krysl, P., "Meshless methods: an. overview and recent developments," Comp. Meth. in Appl. Mech. and Eng. 139, 3-47 (1996).
30. Belytschko, T., Lu, Y. Y., and Gu, L., "Element, free galerkin methods," Int. J. Num. Meth. Eng. 37, 229-256 (1994).
31. Duarte, C. A., and Oden, J. T., "An hp adaptive method using clouds," Comp. Meth. in Appl. Mech. and Eng. 139, 237-262 (1996).
32. Nayroles, B., Touzot, G., and Villon, P., "Generalizing the finite element method: diffuse approximation and diffuse elements," Comp. Mechanics 10, 307-318 (1992).
33. Melenk, J. M., and Babuska, I., "The partition of the unity finite element method," Computer Methods in Applied Meclianics and Engineering 139, 289-314 (1996).
34. Sukumar, N., Moran, B., and Belytschko, T., "The natural element method in solid mechanics," International Journal for Numerical Methods in Engineering 43, 839-887 (1998).
35. Atluri, S. N., and Shen, S. P., The meshless local Petrov-Galerkin (MLPG) method. Tech. Science Press (2002).
36. Atluri, S. N., and Zhu, T., "A new meshless local petrov-galerkin (mlpg) approach in computational mechanics," Computational Mechanics 22, 117-127 (1998).
37. Ferreira, A. J. M., "A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates," Composite Structures 59, 385-392 (2003).
38. Ferreira, A. J. M., "Thick composite beam analysis using a global, meshless approximation based on radial basis functions," Mechanics of Advanced Materials and Structures 10, 271-284 (2003).
39. Rippa, S., "An algorithm for selecting a good value for the parameter c in radial basis function interpolation," Advances in Computational Mathematics 11, 193-210 (1999).
40. Zienkiewicz, O. C., The finite element method. McGraw-Hill (1991).
41. Hughes, T. J. R., The finite element method-Linear static and dynamic finite element analysis. Dover Publications, New York (2000).
42. Bathe, K. J., Finite element procedures in engineering analysis. Prentice Hall (1982).
43. Beatson, R. K., "Fast fitting of radial basis functions: Methods based on preconditioned gmres iteration," Adv. in Comput. Math. 11, 253-270 (1999).
44. Hon, Y. C., and Schaback, R., "On unsymmetric collocation by radial basis functions," Appl. Math. Comput. 119, 177-186 (2001).
45. Wang, B. P., "Parameter optimization in multiquadric response surface approximations," Structural and Multidisciplinary Optimization 26, 219-223 (2004).
46. Schaback, R., and Wendland, H., "Adaptive greedy techniques for approximate solution of large rbf systems," Numer. Algorithms 24, 239-254 (2000).
47. Hon, Y. C., Schaback, R., and Zhou, X., "An adaptive greedy algorithm for solving large rbf collocation problems," Numer. Algorithms 73, 13-25 (2003).
48. Cheng, A. H.-D., Golberg, M. A., Kansa, E. J., and Zammito, G., "Exponential convergence and h-c multiquadric collocation method for partial differential equations," Numer Methods Partial Differential Eq 19, 571-594 (2003).
49. Reddy, J. N., "A simple higher-order theory for laminated composite plates," Journal of Applied Mechanics 51, 745-752 (1984).
50. Reddy, J. N., Mechanics of laminated composite plates. CRC Press, New York (1997).
51. Qian, L. F., Batra, R. C., and Chen, L. M., "Static and dynamic deformations of thick functionaally graded elastic plate by using higher-order shear and normal deformable plate theory and meshless local Petrov-Galerkin method," Composites Part B 35(6-8), 685-697 (2004).
52. Batra, R. C., and Vidoili, S., "Higher order piezoelectric plate theory derived from a three-dimensional variational principle," AIAA Journal 40(1), 91-104 (2002).
53. 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," Composite Structures 69, 449-457 (2005).
54. Gilhooley, D. F., Batra, R. C., McCarthy, J. R., Xiao, M. A., and Gillespie Jr., J. W., "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, 80, 539-552 (2007).