A discontinuous Galerkin Meshfree modeling of material interface

CMES - Computer Modeling in Engineering and Sciences

Volumn 45, Issue 1, 2009, Pages 57-82

  Wang, Dongdong ^a   Sun, Yue ^a   Li, Ling ^a  

^a XIAMEN UNIVERSITY   (China)

Author keywords

Composite material; Discontinuous Galerkin formulation; Gradient jump; Material interface; Meshfree method

Indexed keywords

ADJACENT PATCHES; DISCONTINUOUS GALERKIN; DISCONTINUOUS GALERKIN FORMULATION; ELASTICITY PROBLEMS; FIELD VARIABLES; JUMP CONDITIONS; MATERIAL INTERFACE; MATERIAL INTERFACES; MATERIAL PROPERTY; MESH-FREE METHOD; MESHFREE; MESHFREE MODELING; MESHFREE PARTICLES; NUMERICAL EXAMPLE; PROBLEM DOMAIN; SUB-DOMAINS; VARIATIONAL FORM;

COMPOSITE MATERIALS; COMPOSITE MICROMECHANICS; COMPUTATIONAL MECHANICS; LAGRANGE MULTIPLIERS; TRACTION (FRICTION);

GALERKIN METHODS;

EID: 76249122302     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (51)

1. Atluri, S.N. (2004): The Meshless Local-Petrov-Galerkin Method for Domain & BIE Discretizations, Tech Science Press.
2. Atluri, S.N.; Han, Z.D.; Rajendran, A.M. (2004): A new implementation of the meshless finite volume method, through the MLPG "mixed" approach, CMES: Computer Modeling in Engineering & Sciences, vol.6, pp. 491-514.
3. Atluri, S.N.; Liu, H.T.; Han, Z.D. (2006a): Meshless Local Petrov-Galerkin (MLPG) mixed collocation method for elasticity problems, CMES: Computer Modeling in Engineering & Sciences, vol.14, pp. 141-152.
4. Atluri, S.N.; Liu, H.T.; Han, Z.D. (2006b): Meshless Local Petrov-Galerkin (MLPG) mixed finite difference method for solid mechanics, CMES: Computer Modeling in Engineering & Sciences, vol.15, pp. 1-16.
5. Atluri, S.N.; Shen, S. (2002): The Meshless Local Petrov-Galerkin (MLPG) Method, Tech Science Press.
6. Atluri, S.N.; Zhu, T. (1998): A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics, Computational Mechanics, vol.22, pp. 117-127.
7. Babuška, I.; Banerjee, U.; Osborn, J.E. (2003): Survey of meshless and generalized finite element methods: a unified approach, Acta Numerica . vol.1, pp.1-125 (Pubitemid 41269899)
8. Babuška, I.; Melenk, J.M. (1997): The partition of unity method, International Journal for Numerical Methods in Engineering, vol.40, pp. 537-556.
9. Batra, R.C., Porfiri M.; Spinello D. (2004): Treatment of material discontinuity in two meshless local Petrov-Galerkin (MLPG) formulations of axisymmetric transient heat conduction, International Journal for Numerical Methods in Engineering, vol.61, pp. 2461-2479.
10. Belytschko, T.; Kronggauz, Y.; Organ, D. (1996): Fleming M. Meshless methods, an overview and recent developments, Computer Methods in Applied Mechanics and Engineering, vol.139, pp. 3-47.
11. Belytschko, T.; Lu, Y. Y.; Gu, L. (1994): Element-free Galerkin methods, International Journal for Numerical Methods in Engineering, vol.37, pp. 229-256.
12. Chen, H.B.; Fu, D.J.; Zhang, P.Q. (2007): An investigation of wave propagation with high wave numbers via the regularized LBIEM, CMES: Computer Modeling in Engineering & Sciences, vol.20, pp. 85-98.
13. Chen, J.S.; Pan, C.; Wu, C.T.; Liu, W.K. (1996): Reproducing kernel particle methods for large deformation analysis of nonlinear structures, Computer Methods in Applied Mechanics and Engineering, vol.139, pp. 195-227.
14. Chen, W.H., Chi, C.T.; Lee, M.H. (2009): A novel element-free Galerkin method with uniform background grid for extremely deformed problems, CMES: Computer Modeling in Engineering & Sciences, vol.40, pp. 175-200.
15. Cockburn, B.; Karniadakis, G.; Shu, C. W.; Griebel, M. (2000): Discontinuous Galerkin methods: theory, computation and applications, Lecture Notes in Computational Science and Engineering, Springer, Berlin.
16. Codes, L.W.; Moran, B. (1996): Treatment of material discontinuity in the elementfree Galerkin method, Computer Methods in Applied Mechanics and Engineering, vol.139, pp. 75-89.
17. Duarte, C.A.M.; Oden, J.T. (1996): H-p clouds and h-p meshless method, Numerical Methods for Partial Differential Equations, vol.12: pp. 673-705.
18. Engel, G.; Garikipati, K.; Hughes, T.J.R.; Larson, M.G.; Mazzei, L.; Taylor, R.L. (2002): Continuous/discontinuous finite element approximations of fourthorder elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity, Computer Methods in Applied Mechanics and Engineering, vol.191, pp. 3669-3750.
19. Gingold, R.A.; Monaghan, J.J. (1977): Smoothed Particle Hydrodynamics: theory and application to non-spherical stars, Monthly Notices of the Royal Astronomical Society, vol 181, pp. 375-389.
20. Golberg, M.A.; Chen, C.S. (1998): The method of fundamental solutions for potential, helmholtz and diffusion problems. In Golberg, M. A.(Ed): Boundary Integral Methods: Numerical and Mathematical Aspects, pp. 103-176. WIT Press & Computational Mechanics Publications, Boston, Southampton.
21. Kansa, E.J. (1990): Multiqudrics-a scattered data approximation scheme with applications to computational fluid dynamics-II. Solutions to parabolic, hyperbolic and elliptic partial differential equations, Computers and Mathematics with Applications, vol.19, pp. 147-161.
22. Kosec, G.; Sarler, B. (2008): Local RBF collocation method for Darcy flow, CMES: Computer Modeling in Engineering & Sciences, vol.25, pp. 197-207.
23. Krongauz, Y.; Belytschko, T. (1998): EFG approximation with discontinuous derivatives, International Journal for Numerical Methods in Engineering, vol.41, pp. 1215-1233.
24. Lancaster, P.; Salkauskas, K. (1981): Surfaces generated by moving least squares methods, Mathematics of Computation, vol.37, pp. 141-158.
25. Li, Q.; Shen, S.; Han, Z.D.; Atluri, S.N. (2003): Application of meshless local Petrov-Galerkin (MLPG) to problems with singularities, and material discontinuities, in 3-D elasticity, CMES: Computer Modeling in Engineering & Sciences, vol.4, pp. 571-586.
26. Li, S.; Atluri, S.N. (2008a): Topology-optimization of structures based on the MLPG mixed collocation method, CMES: Computer Modeling in Engineering & Sciences, vol.26, pp. 61-74.
27. Li, S.; Atluri, S.N. (2008b): The MLPG mixed collocation method for material orientation and topology optimization of anisotropic solids and structures, CMES: Computer Modeling in Engineering & Sciences, vol.30, pp. 37-56.
28. Li, S.; Liu, W.K. (2004): Meshfree and Particle Methods, Springer-Verlag.
29. Liu, C.S. (2008): Improving the ill-conditioning of the method of fundamental solutions for 2d Laplace equation. CMES: Computer Modeling in Engineering and Sciences, vol.28, pp. 77-93.
30. Liu, D.; Zheng X.; Lu Y. (2009): A discontinuous Galerkin finite element method for heat conduction problems with local high gradient and thermal contact resistance, CMES: Computer Modeling in Engineering & Sciences, vol.39, pp. 263-300.
31. Liu, G.R. (2002): Mesh Free Methods: Moving Beyond the Finite Element Method, CRC Press.
32. Liu, W.K., Jun, S.; Zhang, Y.F. (1995): Reproducing kernel particle methods, International Journal for Numerical Methods in Fluids, vol.20, pp. 1081-1106.
33. Liu, W.K.; Han, W.; Lu, H.; Li, S.; Cao, J. (2004): Reproducing kernel element method Part I. theoretical formulation, Computer Methods in Applied Mechanics and Engineering, vol.193, pp. 933-951.
34. Lucy, L. (1977): A numerical approach to the testing of the fission hypothesis, Astronomical Journal, vol.82, pp. 1013-1024.
35. Marin, L. (2008): The method of fundamental solutions for inverse problems associated with the steady-state heat conduction in the presence of sources. CMES: Computer Modeling in Engineering and Sciences, vol.30, pp. 99-122.
36. Masuda, S.; Noguchi, H. (2006): Analysis of structure with material interface by meshfree method, CMES: Computer Modeling in Engineering & Sciences, vol.11, pp. 131-143.
37. Mohammadi, M.H. (2008): Stabilized meshless local Petrov-Galerkin (MLPG) method for incompressible viscous fluid flows, CMES: Computer Modeling in Engineering & Sciences, vol.29, pp. 75-94.
38. Monaghan, J. J. (2005): Smoothed particle hydrodynamics. Reports on Progress in Physics, vol.68, pp. 1703-1759.
39. Nayroles, B.; Touzot, G.; Villon, P. (1992): Generalizing the finite element method: diffuse approximation and diffuse elements, Computational Mechanics, vol.10, pp. 307-318.
40. Oden, J.T.; Babuška, I.; Baumann, C.E. (1998): A discontinuous hp finite element method for diffusion problems, Journal of Computational Physics, vol.146, pp. 491-519.
41. Pini, G.; Mazzia, A.; Sartoretto, F. (2008): Accurate MLPG solution of 3D po tential problems, CMES: Computer Modeling in Engineering & Sciences, vol.36, pp. 43-64.
42. Sellountos, E. J.; Sequeira, A.; Polyzos, D. (2009): Elastic transient analysis with MLPG(LBIE) method and local RBFs, CMES: Computer Modeling in Engineering & Sciences, vol.41, pp. 215-241.
43. Sethuraman, R.; Rajesh, N.R. (2009): Evaluation of elastic-plastic crack tip parameters using partition of unity finite element method and pseudo elastic analysis, CMES: Computer Modeling in Engineering & Sciences, vol.39, pp. 67-100.
44. Sladek, J.; Sladek, V.; Solek, P.; Atluri, S.N. (2008): Modeling of intelligent material systems by the MLPG, CMES: Computer Modeling in Engineering & Sciences, vol.34, pp. 273-300.
45. Sukumar, N.; Moran, B.; Belytschko, T. (1998): The natural element method in solid mechanics, International Journal for Numerical Methods in Engineering, vol.43, pp. 839-887.
46. Wang, D.; Chen, J.S.; Sun, L. (2003): Homogenization of magnetostrictive particlefilled elastomers using meshfree method with interface discontinuity, Finite Elements in Analysis and Design, vol.39, pp. 765-782.
47. Wen, P.H.; Aliabadi, M.H.; Lin, Y.W. (2008): Meshless method for crack analysis in functionally graded materials with enriched radial base functions, CMES: Computer Modeling in Engineering & Sciences, vol.30, pp. 133-147.
48. Wong, S.; Shie, Y. (2008): Large deformation analysis with Galerkin based smoothed particle hydrodynamics, CMES: Computer Modeling in Engineering & Sciences, vol.36, pp. 97-118.
49. Wu, C.P.; Chin, K.H.; Wang, Y.M. (2008): A differential reproducing kernel particle method for the analysis of multilayered elastic and piezoelectric plates, CMES: Computer Modeling in Engineering & Sciences, vol.27, pp. 163-186.
50. Zhu T.; Zhang J.; Atluri, S.N. (1998): A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach, Computational Mechanics, vol.21, pp. 223-235. (Pubitemid 128566412)
51. Zienkiewicz, O. C.; Taylor, R. L.; Sherwin, S. J.; Peiro, J. (2003): On discontinuous Galerkin methods, International Journal for Numerical Methods in Engineering, vol.58, pp. 1119-1148.