Boundary element analysis of three-dimensional exponentially graded isotropic elastic solids

CMES - Computer Modeling in Engineering and Sciences

Volumn 22, Issue 2, 2007, Pages 151-164

  Criado, R ^a   Ortiz, J E ^a   Mantic V ^a   Gray, L J ^a,b   Paris E ^a  

^a UNIVERSITY OF SEVILLE   (Spain)

^b OAK RIDGE NATIONAL LABORATORY   (United States)

Author keywords

Boundary element method; Functionally graded materials; Fundamental solution in tractions; Somigliana identity; Three dimensional elasticity

Indexed keywords

BOUNDARY ELEMENT METHOD; ELASTICITY; GALERKIN METHODS; NUMERICAL METHODS; PROBLEM SOLVING;

FUNDAMENTAL SOLUTION IN TRACTIONS; ISOTROPIC SOLIDS; SOMIGLIANA IDENTITY; THREE DIMENSIONAL ELASTICITY;

FUNCTIONALLY GRADED MATERIALS;

EID: 36448947633     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (32)

1. Aliabadi, M.H. (2002): The Boundary Element Method, Volume 2 Applications in Solids and Structures. John Wiley & Sons, Chichester.
2. Anlas, G.; Santare, M.H.; Lambros, J. (2000): Numerical calculation of stress intensity factors in functionally graded materials. International Journal of Fracture, vol. 104, pp. 131-143.
3. Atluri, S.N.; Shen, S. (2002): The meshless local Petrov-Galerkin (MLPG) method: A simple & less costly alternative to the finite element and boundary element method. CMES: Computer Modeling in Engineering & Sciences, vol. 3, pp. 11-52.
4. Berger, J.R.; Martin, P.A.; Mantič, V.; Gray, L.J. (2005): Fundamental solution for steady-state heat transfer in an exponentially graded anisotropic material. ZAMP, vol. 56, pp. 293-303.
5. Chan, Y.; Gray, L.J.; Kaplan, T.; Paulino, G.H. (2004): Green's function for a two-dimensional exponentially graded elastic medium. Proceedings Royal Society London A, vol. 460, pp. 1689-1706.
6. Ching, H.K.; Chen, J.K. (2006): Thermomechanical analysis of functionally graded composites under laser heating by the MLPG method. CMES: Computer Modeling in Engineering & Sciences, vol. 13, pp. 199-218.
7. Clements, D.L. (1998): Fundamental solutions for second order linear elliptic partial differential equations. ComputationalMecahnics, vol. 22, pp. 26-31.
8. Clements, D.L.; Budhi, W.S. (1999): A boundary element method of the solution of a class of steady-state problems for anisotropic media. Journal of Heat Transfer, vol. 121, pp. 462-465.
9. Costabel, M.; Dauge, M. (1997): On representation formulas and radiation conditions. Mathematical Methods in the Applied Sciences, vol. 20, pp. 133-150.
10. Criado, R. (2005): Desarrollo y programación de la solución fundamental en desplazamientos y tensiones para el problema elástico tridimensional en materiales exponencialmente graduados isótropos. Proyecto Fin de Carrera, ETSI, Universidad de Sevilla.
11. Criado, R.; Gray, L.J.; Mantič, V.; París, F. (2008): Green's function evaluation for three dimensional exponentially graded elasticity. International Journal for Numerical Methods in Engineering (in press).
12. Gray, L.J.; Kaplan, T; Richardson, J.D.; Paulino, G.H. (2003): Green's function and boundary integral analysis for exponentially graded materials: heat conduction. Journal of Applied Mechanics, vol. 40, pp. 543-549.
13. Han, F.; Pan, E.; Roy, A.K.; Yue, Z.Q. (2006): Responses of piezoelectric, transversely isotropic, functionally graded, and multilayered half spaces to uniform circular surface loadings. CMES: Computer Modeling in Engineering & Sciences, vol. 14, pp. 15-30.
14. Kim, J.; Paulino, G.H. (2002a): Finite element evaluation of mixed mode stress intensity factors in functionally graded materials. International Journal for Numerical Methods in Engineering, vol. 53, pp. 1903-1935.
15. Kim, J.; Paulino, G.H. (2002b): Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials. Journal of Applied Mechanics, vol. 69, pp. 502-514.
16. Kuo, H.Y.; Chen, T. (2005): Steady and transient Greens functions for anisotropic conduction in an exponentially graded solid. International Journal of Solids and Structures, vol. 42, pp. 1111-1128.
17. Lachat, J.C.; Watson, J.O. (1976): Effective numerical treatment of boundary integral equations: a formulation for three-dimensional elastostatics. International Journal for Numerical Methods in Engineering, vol.10, pp. 991-1005.
18. Lee, Y.-D.; Erdogan, F. (1998): Interface cracking of FGM coatings under steady-state heat flow. Engineering Fracture Mechanics, vol. 59, pp. 361-380.
19. Mantič, V. (1993): A new formula for the C-matrix in the Somigliana identity. Journal of Elasticity, vol. 33, pp. 191-201.
20. Martin, P.A.; Richardson, J.D.; Gray, L.J.; Berger, J.R. (2002): On Green's function for a three-dimensional exponentially graded elastic solid. Proceedings Royal Society London A, vol. 458,pp. 1931-1947.
21. Núñez, J.P.; Mantič, V.; París, F.; Berger, J. (2002): Boundary element analysis of heat transfer at an interface crack in an FGM coating. In ECCM-10, Composites for the Future, 10th European Conference on Composite Materials (CD), The European Society for Composite Materials (ESCM), Brugge.
22. París, F.; Cañas, J. (1997): Boundary Element Method, Fundamentals and Applications. Oxford University Press, Oxford.
23. Paulino, G.H.; Kim, J. (2004): A new approach to compute T-stress in functionally graded materials by means of the interaction integral method. Engineering Fracture Mechanics, vol. 71, pp. 1907-1950.
24. Paulino, G.H.; Sutradhar, A.; Gray, L.J. (2002): Boundary element methods for functionally graded materials. In S.A. Kinnas (Ed.) IABEM 2002 (CD), The University of Texas at Austin.
25. Santare, M.H.; Lambros, J. (2000): Use of graded finite elements to model the behavior of nonhomogeneous materials. Journal of Applied Mechanics, vol. 67, pp. 819-822.
26. Seyrafian, S.; Gatmiri, B.; Noorzad, A. (2006): Green functions for a continuously nonhomogeneous saturated media. CMES: Computer Modeling in Engineering & Sciences, vol. 15, pp. 115-126.
27. Shaw, R.P.; Makris, N. (1992): Green's function for Helmholtz and Laplace equations in heterogeneous media. Engineering Analysis with Boundary Elements, vol. 10, pp. 179-183.
28. Sládek, J.; Sládek, V.; Kriváček, J.; Zhang, Ch. (2005): Meshless local Petrov-Galerkin method for stress and crack analysis in 3-D axisymmetric FGM bodies. CMES: Computer Modeling in Engineering & Sciences, vol. 8, pp. 259-270.
29. Sládek, J.; Sládek, V.; Zhang, Ch. (2004): Application of meshless local Petrov-Galerkin (MLPG) method to elastodynamic problems in continuously nonhomogeneous solids. CMES: Computer Modeling in Engineering & Sciences, vol. 4, pp. 637-648.
30. Sládek, J.; Sládek, V.; Zhang, Ch., Solek, P.; Starek, L. (2007): Fracture analyses in continuously nonhomogeneous piezoelectric solids by the MLPG. CMES: Computer Modeling in Engineering & Sciences, vol. 19, pp. 247-262.
31. Sutradhar, A.; Paulino, G. H. (2004): The simple boundary element method for transient heat conduction in functionally graded materials. Computer Methods in Applied Mechanics and Engineering, vol. 193, pp. 4511-4539.
32. Suresh, S.; Mortensen A. (1998): Fundamentals of Functionally Graded Materials. IOM Communications, London.