A parallel domain decomposition BEM algorithm for three-dimensional exponentially graded elasticity

Journal of Applied Mechanics, Transactions ASME

Volumn 75, Issue 5, 2008, Pages 0511081-0511088

  Ortiz, J E ^a   Shelton, W A ^b   Mantic V ^a   Criado, R ^b   Gray, L J ^a   Paris F ^b  

^a UNIVERSITY OF SEVILLE   (Spain)

^b OAK RIDGE NATIONAL LABORATORY   (United States)

Author keywords

Boundary integral equation; Distributed computing; Domain decomposition; Functionally graded material; Radially graded material

Indexed keywords

ANALYTICAL SOLUTIONS; AXISYMMETRIC; BOUNDARY INTEGRAL EQUATION; BOUNDARY INTEGRALS; COMPUTATIONAL COSTS; CYLINDRICAL GEOMETRIES; DISTRIBUTED COMPUTING; DOMAIN DECOMPOSITION; FUNCTIONALLY GRADED; FUNCTIONALLY GRADED MATERIAL; GRADED MATERIALS; NUMERICA L RESULTS; PARALLEL DOMAIN DECOMPOSITION; PLANE STRAINS; RADIALLY GRADED MATERIAL; SUB DOMAINS;

BEAMS AND GIRDERS; DIFFERENTIAL EQUATIONS; DOMAIN DECOMPOSITION METHODS; ELASTICITY; FUNCTIONALLY GRADED MATERIALS; GREEN'S FUNCTION; INTEGRAL EQUATIONS; THREE DIMENSIONAL;

PARALLEL ALGORITHMS;

EID: 52649086343     PISSN: 00218936     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2936232     Document Type: Conference Paper

References (42)

1. Miyamoto, Y., Kaysser, W. A., Rabin, B. H., Kawasaki, A., and Ford, R. G., 1999, Functionally Graded Materials: Design, Processing and Applications, Kluwer Academic, Dordrecht.
2. Suresh, S., and Mortensen, A., 1998, Fundamentals of Functionally Graded Materials, The Institute of Materials, IOM Communications Ltd., London.
3. Kim, J.-H., and Paulino, G. H., 2002, "Finite Element Evaluation of Mixed-Mode Stress Intensity Factors in Functionally Graded Materials," Int. J. Numer. Methods Eng., 53, pp. 1903-1935.
4. Kim, J.-H., and Paulino, G. H., 2002, "Mixed-Mode Fracture of Orthotropic Functionally Graded Materials Using the Finite Element Method," Eng. Fract. Mech., 69, pp. 1769-1790.
5. Kim, J.-H., and Paulino, G. H., 2002, "Isoparametric Graded Finite Elements for Nonhomogeneous Isotropic and Orthotropic Materials," ASME J. Appl. Mech., 69, pp. 502-514.
6. Silva, E. C. N., Carbonari, R. C., and Paulino, G. H., 2007, "On Graded Elements for Multiphysics Applications," Smart Mater. Struct., 16, pp. 2408-2428.
7. Naghdabadi, R., and Kordkheili, S. A. H., 2005, "A Finite Element Formulation for Analysis of Functionally Graded Plates and Shells," Arch. Appl. Mech., 74, pp. 375-386.
8. Anlas, G., Santare, M. H., and Lambros, J., 2000, "Numerical Calculation of Stress Intensity Factors in Functionally Graded Materials," Int. J. Fract., 104, pp. 131-143.
9. Santare, M. H., and Lambros, J., 2000, "Use of Graded Finite Elements to Model the Behavior of Nonhomogeneous Materials," ASME J. Appl. Mech., 67, pp. 819-822.
10. Erdogan, F., 1995, "Fracture Mechanics of Functionally Graded Materials," Composites Eng., 5, pp. 753-770.
11. Konda, N., and Erdogan, F., 1994, "The Mixed Mode Crack Problem in a Nonhomogeneous Elastic Medium," Eng. Fract. Mech., 47, pp. 533-545.
12. Lee, Y. D., and Erdogan, F., 1994, "Residual/Thermal Stresses in FGM and Laminated Thermal Barrier Coatings," Int. J. Fract., 69, pp. 145-165.
13. Erdogan, F., and Bahar, L. Y., 1964, "On the Solution of Simultaneous Dual Integral Equations," J. Soc. Ind. Appl. Math., 12 pp. 666-675.
14. Kaya, A. C., and Erdogan, F., 1987, "On the Solution of Integral Equations With a Generalized Cauchy Kernel," Q. Appl. Math., 45, pp. 455-469.
15. Kaya, A. C., and Erdogan, F., 1987, "On the Solution of Integral Equations With Strongly Singular Kernels," Q. Appl. Math., 45, pp. 105-122.
16. París, F., and Cañas, J., 1997, Boundary Element Method: Fundamentals and Applications, Oxford University Press, Oxford.
17. Bonnet, M., 1998, Boundary Integral Equation Methods for Solids and Fluids, Wiley, England.
18. Aliabadi, M. H., 2002, The Boundary Element Method, Vol. II, Wiley, Chichester.
19. Chan, Y.-S., Gray, L. J., Kaplan, T., and Paulino, G. H., 2004, "Green's Function for a Two-Dimensional Exponentially Graded Elastic Medium," Proc. R. Soc. London, Ser. A, 460, pp. 1689-1706.
20. Martin, P. A., Richardson, J. D., Gray, L. J., and Berger, J., 2002, "On Green's Function for a Three-Dimensional Exponentially-Graded Elastic Solid," Proc. R. Soc. London, Ser. A, 458, pp. 1931-1948.
21. Criado, R., Gray, L. J., Mantič, V., and París, F., 2008, "Green's Function Evaluation for Three Dimensional Exponentially Graded Elasticity," Int. J. Numer. Methods Eng., 74, pp. 1560-1591.
22. Criado, R., Ortiz, J. E., Mantič, V., Gray, L. J., and París, F., 2007, "Boundary Element Analysis of Three-Dimensional Exponentially Graded Isotropic Elastic Solids," Comput. Model. Eng. Sci., 22, pp. 151-164.
23. Mantič, V., 1993, "A New Formula for the C-Matrix in the Somigliana Identity," J. Elast., 33, pp. 191-201.
24. Araújo, F. C., Silva, K. I., and Telles, J. C. F., 2006, "Generic Domain Decomposition and Iterative Solvers for 3-D BEM Problems," Int. J. Numer. Methods Eng., 68, pp. 448-472.
25. Araújo, F. C., Silva, K. I., and Telles, J. C. F., 2007, "Application of a Generic Domain-Decomposition Strategy to Solve Shell-Like Problems Through 3D BE Models," Commun. Numer. Methods Eng., 23, pp. 771-785.
26. Kamiya, N., Iwase, H., and Kite, E., 1996, "Parallel Implementation of Boundary Element Method With Domain Decomposition," Eng. Anal. Boundary Elem., 18, pp. 209-216.
27. Kamiya, N., Iwase, H., and Kite, E., 1996, "Performance Evaluation of Parallel Boundary Element Analysis by Domain Decomposition Method," Eng. Anal. Boundary Elem., 18, pp. 217-222.
28. Divo, E., Kassab, A. J., and Rodriguez, F., 2003, "Parallel Domain Decomposition Approach for Large-Scale Three-Dimensional Boundary-Element Models in Linear and Nonlinear Heat Conduction," Numer. Heat Transfer, Part B, 44, pp. 417-437.
29. Ingber, M. S., Schmidt, C. C., Tanski, J. A., and Phillips, J., 2003, "Boundary-Element Analysis of 3-D Diffusion Problems Using a Parallel Domain Decomposition Method," Numer. Heat Transfer, Part B, 44, pp. 145-164.
30. Zhang, X., and Hasebe, N., 1999, "Elasticity Solution for a Radially Nonhomogeneous Hollow Circular Cylinder," ASME J. Appl. Mech., 66, pp. 598-606.
31. Maier, G., Diligenti, M., and Carini, A., 1991, "A Variational Approach to Boundary Element Elastodynamic Analysis and Extension to Multidomain Problems," Comput. Methods Appl. Mech. Eng., 92, pp. 193-213.
32. Hölzer, S. M., 1992, "The Symmetric Galerkin BEM for Plane Elasticity: Scope and Applications," Numerical Methods in Engineering, C. Hirsch, ed., Elsevier, New York.
33. Gray, L. J., and Paulino, G. H., 1997, "Symmetric Galerkin Boundary Integral Formulation for Interface and Multi-Zone Problems," Int. J. Numer. Methods Eng., 40, pp. 3085-3101.
34. Blázquez, A., París, F., and Mantǐ, V., 1998, "BEM Solution of Two Dimensional Contact Problems by Weak Application of Contact Conditions With Non-Conforming Discretizations," Int. J. Solids Struct., 35, pp. 3259-3278.
35. Li, X. S., 2005, "An Overview of SuperLU: Algorithms, Implementation, and User Interface," ACM Trans. Math. Softw., 31, pp. 302-325.
36. Saad, Y., 2003, Iterative Methods for Sparse Linear Systems, 2nd ed., SIAM, Philadelphia.
37. Barber, J. R., 1992, Elasticity, Kluwer Academic, Dordrecht.
38. Wacker, G., Bledzki, A. K., and Chate, A., 1998, "Effect of Interphase on the Transverse Young's Modulus of Glass/Epoxy Composites," Composites, Part A, 29A, pp. 619-626.
39. Jasiuk, I., and Kouider, M. W., 1993, "The Effect of an Inhomogeneous Interphase on the Elastic Constants of Transversely Isotropic Composites," Mech. Mater., 15, pp. 53-63.
40. Liu, Y., and Xu, N., 2000, "Modeling of Interphase Cracks in Fiber-Reinforced Composites With the Presence of Interphases Using the Boundary Element Method," Mech. Mater., 32, pp. 769-783.
41. Luo, J. F., Liu, Y., and Berger, E. J., 2000, "Interfacial Stress Analysis for Multi-Coating Systems Using an Advanced Boundary Element Method," Comput. Mech., 24, pp. 448-455.
42. Abramowitz, M., and Stegun, I. A., 1972, Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables, Dover, New York.