Modelling elasto-plasticity using the hybrid MLPG method

CMES - Computer Modeling in Engineering and Sciences

Volumn 56, Issue 2, 2010, Pages 153-176

  Heaney, Claire ^a   Augarde, Charles ^a   Deeks, Andrew ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

Author keywords

Elasto plasticity; Meshfree; Meshless; Meshless local Petrov Galerkin

Indexed keywords

ELASTOPLASTIC MATERIALS; FINITE BOUNDARY; GEOMECHANICS; MESH-LESS METHODS; MESHFREE; MESHLESS; MESHLESS LOCAL PETROV-GALERKIN; MESHLESS LOCAL PETROV-GALERKIN METHOD; MLPG METHOD;

ELASTOPLASTICITY; FINITE ELEMENT METHOD; GALERKIN METHODS;

PLASTICITY;

EID: 77951199272     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (46)

1. Andreaus, U.; Batra, R.; Porfiri, M. (2005): Vibrations of cracked Euler-Bernoulli beams using Meshless Local Petrov-Galerkin (MLPG) method. CMES-Computer Modeling in Engineering & Sciences, vol.9, no.2, pp.111-131. (Pubitemid 41375230)
2. Askes, H.; de Borst, R.; Heeres, O. (1999): Conditions for locking-free elasto-plastic analyses in the Element-Free Galerkin method. Comput. Methods Appl. Mech. Engrg., vol.173, no.1-2, pp.99-109.
3. Atluri, S.; Liu, H.; Han, Z. (2006): Meshless Local Petrov-Galerkin (MLPG) Mixed Finite Difference Method for Solid Mechanics. CMES-Computer Modeling in Engineering & Sciences, vol.15, pp.1-16. (Pubitemid 44562735)
4. Atluri, S. N.; Shen, S. P. (2002): The meshless local Petrov-Galerkin (MLPG) method: A simple & less-costly alternative to the finite element and boundary element methods. CMES-Computer Modeling in Engineering & Sciences, vol.3, no.1, pp.11-51.
5. Atluri, S. N.; Zhu, T. (1998): A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput. Mech., vol.22, pp.117-127. (Pubitemid 128620889)
6. Barry, W.; Saigal, S. (1999): A three-dimensional element-free Galerkin elastic and elastoplastic formulation. Int. J. Numer. Meth. Eng., vol.46, no.5, pp.671-693. (Pubitemid 29509090)
7. Batra, R. C.; Porfiri, M. (2008): Analysis of rubber-like materials using meshless local Petrov-Galerkin (MLPG) method. Commun. Numer. Meth. En., vol.24, no.12, Sp. Iss. SI, pp.1781-1804.
8. Belinha, J.; Dinis, L. M. (2006): Elasto-plastic analysis of plates by the element free Galerkin method. Eng. Comp., vol.23, no.5-6, pp.525-551. (Pubitemid 44035691)
9. Belytschko, T.; Lu, Y. Y.; Gu, L. (1994): Element-free Galerkin methods. Int. J. Numer. Meth. Eng., vol.37, pp.229-256.
10. Bergamaschi, L.; Martinez, A.; Pini, G. (2009): An Efficient Parallel MLPG Method for Poroelastic Models. CMES-Computer Modeling in Engineering & Sciences, vol.49, no.3, pp.191-215.
11. Deeks, A.; Augarde, C. (2005): A meshless local Petrov-Galerkin scaled boundary method. Comput. Mech., vol.36, pp.159-170. (Pubitemid 40920864)
12. Deeks, A. J.; Augarde, C. E. (2007): A hybrid meshless local Petrov-Galerkin method for unbounded domains. Comput. Methods Appl. Mech. Engrg., vol.196, no.4-6, pp.843-852. (Pubitemid 44644870)
13. Feng, W. J.; Han, X.; Li, Y. S. (2009): Fracture Analysis for Two-dimensional Plane Problems of Nonhomogeneous Magneto-electro-thermo-elastic Plates Subjected to Thermal Shock by Using the Meshless Local Petrov-Galerkin Method. CMES-Computer Modeling in Engineering & Sciences, vol.48, no.1, pp.1-26.
14. Fernandez-Mendez, S.; Huerta, A. (2004): Imposing essential boundary conditions in mesh-free methods. Comput. Methods Appl. Mech. Engrg., vol.193, pp.1257-1275. (Pubitemid 38439214)
15. Fries, T.; Matthies, H. (2004): Classification and overview of meshfree methods. Technical Report 2003-3, Technical University Braunschweig, Brunswick, Germany, 2004.
16. Han, Z.; Atluri, S. (2004): Meshless Local Petrov-Galerkin (MLPG) approaches for solving 3D Problems in elasto-statics. CMES-Computer Modeling in Engineering & Sciences, vol.6, pp.169-188.
17. Han, Z.; Rajendran, A.; Atluri, S. (2005): Meshless Local Petrov-Galerkin (MLPG) approaches for solving nonlinear problems with large deformations and rotations. CMES-Computer Modeling in Engineering & Sciences, vol.10, no.1, pp.1-12.
18. Hazama, O.; Okuda, H.; Wakatsuchi, K. (2001): A digital systematization of meshfree method and its applications to elasto-plastic infinitesimal deformation analysis. Adv. Eng. Softw., vol.32, no.8, pp.647-664.
19. Hill, R. (1950): The Mathematical Theory of Plasticity. Clarendon Press, Oxford.
20. Jarak, T.; Soric, J. (2008): Analysis of rectangular square plates by the mixed Meshless Local Petrov-Galerkin (MLPG) approach. CMES-Computer Modeling in Engineering & Sciences, vol.38, no.3, pp.231-261.
21. Kargarnovin, M.; Toussi, H.; Fariborz, S. (2004): Elasto-plastic element-free Galerkin method. Comput. Mech., vol.33, no.3, pp.206-214.
22. Kasper, T.; Meschke, G. (2004): A 3D finite element simulation model for TBM tunnelling in soft ground. Int. J. Numer. Anal. Methods Geomech., vol.28, no.14, pp.1441-1460. (Pubitemid 39587907)
23. Lancaster, P.; Salkauskas, K. (1981): Surfaces generated by moving least squares methods. Math. Comput., vol.37, pp.141-158.
24. Liu, W.; Jun, S.; Li, S.; Adee, J.; Belytschko, T. (1995): Reproducing kernel particle methods for structural dynamics. Int. J. Numer. Meth. Eng., vol.38, no.10, pp.1655-1679.
25. Long, S. Y.; Liu, K. Y.; Li, G. Y. (2008): An analysis for the elasto-plastic fracture problem by the meshless local Petrov-Galerkin method. CMES-Computer Modeling in Engineering & Sciences, vol.28, no.3, pp.203-216.
26. Monaghan, J. (1988): An introduction to SPH. Comput. Phys. Comm., vol.48, pp.89-96.
27. Nayroles, B.; Touzot, G.; Villon, P. (1992): Generalizing the finite element method: diffuse approximation and diffuse elements. Comput. Mech., vol.10, pp.307-318.
28. Nguyen, V. P.; Rabczuk, T.; Bordas, S.; Duflot, M. (2008): Meshless methods: A review and computer implementation aspects. Math. Comput. Simulat., vol.79, no.3, pp.763-813.
29. Nie, Y.; Atluri, S.; Zuo, C. (2006): The optimal radius of the support of radial weights used in moving least squares approximation. CMES-Computer Modeling in Engineering & Sciences, vol.12, pp.137-147.
30. Pamin, J.; Askes, H.; de Borst, R. (2003): Two gradient plasticity theories discretized with the element-free Galerkin method. Comput. Methods Appl. Mech. Engrg., vol.192, no.20-21, pp.2377-2403.
31. Pannachet, T.; Askes, H. (2000): Some observations on the enforcement of constraint equations in the EFG method. Commun. Numer. Methods Eng., vol.16, no.12, pp.819-830.
32. Pini, G.; Mazzia, A.; Sartoretto, F. (2008): Accurate MLPG solution of 3d potential problems. CMES-Computer Modeling in Engineering & Sciences, vol.36, pp.43-64.
33. Seyrafian, S.; Gatmiri, B.; Noorzad, A. (2007): Analytical Investigation of Depth Non-homogeneity Effect on the Dynamic Stiffness of Shallow Foundations. CMES-Computer Modeling in Engineering & Sciences, vol.21, pp.209-217.
34. Sheng, D.; Nazem, M.; Carter, J. P. (2009): Some computational aspects for solving deep penetration problems in geomechanics. Comput. Mech., vol.44, no.4, pp.549-561.
35. Simo, J. C.; Hughes, T. J. R. (1998): Computational Inelasticity. Interdisciplinary Applied Mathematics: Mechanics and Materials. Springer.
36. Sladek, J.; Sladek, V.; Krivacek, J.; Wen, P. H.; Zhang, C. (2007): Meshless local Petrov-Galerkin (MLPG) method for Reissner-Mindlin plates under dynamic load. Comput. Method. Appl. M., vol.196, no.25-28, pp.2681-2691.
37. Sladek, J.; Sladek, V.; Solek, P. (2009): Elastic analysis in 3D anisotropic functionally graded solids by the MLPG. CMES-Computer Modeling in Engineering & Sciences, vol.43, no.3, pp.223-251.
38. Sladek, J.; Sladek, V.; Solek, P.; Atluri, S. (2008): Modeling of Intelligent Material Systems by the MLPG. CMES-Computer Modeling in Engineering & Sciences, vol.34, pp.273-300.
39. Sladek, J.; Sladek, V.; Solek, P.; Pan, E. (2008): Fracture analysis of cracks in magneto-electro-elastic solids by the MLPG. Comput. Mech., vol.42, no.5, pp.697-714.
40. Sladek, J.; Sladek, V.; Solek, P.; Tan, C. L.; Zhang, C. (2009): Two-and Three-Dimensional Transient Thermoelastic Analysis by the MLPG Method. CMES-Computer Modeling in Engineering & Sciences, vol.47, no.1, pp.61-95.
41. Soares, D.; Sladek, J.; Sladek, K. (2009): Dynamic Analysis by Meshless Local Petrov-Galerkin Formulations Considering a Time-Marching Scheme Based on Implicit Green's Functions. CMES-Computer Modeling in Engineering & Sciences, vol.50, pp.115-140.
42. Sterk, M.; Trobec, R. (2008): Meshless solution of a diffusion equation with parameter optimization and error analysis. Eng. Anal. Bound. Elem., vol.32, pp.567-577.
43. Wang, L.; Daniewicz, S.; Horstemeyer, M.; Sintay, S.; Rollett, A. (2009): Three-dimensional finite element analysis using crystal plasticity for a parameter study of fatigue crack incubation in a 7075 aluminum alloy. Int. J. Fatigue, vol.31, no.4, pp.659-667.
44. Wu, C.; Chen, J.; Chi, L.; Huck, F. (2001): Lagrangian meshfree formulation for analysis of geotechnical materials. J. Eng. Mech-ASCE, vol.127, no.5, pp.440-449. (Pubitemid 32464256)
45. Xiong, Y. B.; Long, S. Y.; Liu, K. Y.; Li, G. Y. (2006): A meshless local Petrov-Galerkin method for elasto-plastic problems. In Liu, GR and Tan, VBC and Han, X(Ed): Computational Methods, Pts 1 and 2, pp.1477-1482.1st International Conference on Computational Methods (ICCM04), Singapore, Dec 15-17, 2004.
46. Zhuang, X.; Augarde, C. E. (2010): Aspects of the use of orthogonal basis functions in the element free Galerkin method. Int. J. Numer. Meth. Eng., vol.81(3), pp.366-380.