Nonlinear dynamic analysis of three-dimensional elasto-plastic solids by the meshless local Petrov-Galerkin (MLPG) method

Computers, Materials and Continua

Volumn 29, Issue 1, 2012, Pages 15-39

  Rezaei Mojdehi, A ^a,b   Darvizeh, A ^c   Basti, A ^b  

^a NIROO RESEARCH INSTITUTE   (Iran)

^b UNIVERSITY OF GUILAN   (Iran)

^c ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

Meshless Local Petrov Galerkin method; Nonlinear Dynamic Analysis; Normality Hypothesis of Plasticity; Three Dimensional Moving Least Square approximation

Indexed keywords

CONSISTENCY CONDITIONS; ELASTO-PLASTIC ANALYSIS; ELASTO-PLASTIC PROBLEM; ELASTOPLASTIC SOLIDS; FIELD VARIABLES; GALERKIN; GENERAL DYNAMICS; GOVERNING EQUATIONS; LEAST SQUARES; LOCAL INTEGRAL EQUATIONS; LOCAL WEAK FORM; MESHLESS LOCAL PETROV-GALERKIN APPROACHES; MESHLESS LOCAL PETROV-GALERKIN METHOD; MESHLESS LOCAL PETROV-GALERKIN METHODS; MOVING LEAST SQUARE APPROXIMATION; NUMERICAL APPROACHES; NUMERICAL EXAMPLE; PLASTIC MULTIPLIERS; PROBLEM DOMAIN; SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS; SHAPE FUNCTIONS; STRESS STRAIN RELATION; SUB-DOMAINS; THREE DIMENSIONAL SPACE; TIME INTEGRATION METHODS; UNIT TESTS; VON MISES YIELD CRITERION; WEAK FORMULATION; YIELD FUNCTION;

DYNAMICS; ELASTOPLASTICITY; GALERKIN METHODS; LEAST SQUARES APPROXIMATIONS; PLASTICITY;

THREE DIMENSIONAL;

EID: 84865161003     PISSN: 15462218     EISSN: 15462226     Source Type: Journal    
DOI: None     Document Type: Article

References (47)

1. Atluri, S. N.; Cho, J. Y.; Kim, H. G. (1999): Analysis of thin beams, using the meshless local Petrov-Galerkin method, with generalized moving least squares interpolations. CMES: Computer Modeling in Engineering & Sciences, vol. 24, no. pp. 334-347. (Pubitemid 30546708)
2. Atluri, S. N.; Kim, H. G.; Cho, J. Y. (1999): A critical assessment of the truly meshless local Petrov-Galerkin (MLPG), and local boundary integral equation (LBIE) methods. Comput. Mech., vol. 24, no. pp. 348-372. (Pubitemid 30546709)
3. Atluri, S. N.; Shen, S. (2002a): 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. pp. 11-52.
4. Atluri, S. N.; Shen, S. (2002b): The Meshless Local Petrov-Galerkin (MLPG) Method. Tech Science Press
5. Atluri, S. N.; Zhu, T. (1998): A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput. Mech., vol. 22, no. pp. 117-127. (Pubitemid 128620889)
6. Atluri, S. N.; Zhu, T. (2000): The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics. Comput. Mech., vol. 25, no. pp. 169-179. (Pubitemid 30593735)
7. Babuska, I.; Melenk, J. (1997): The partition of unity method. int. J. Numer. Methods Engrg., vol. 40, no. pp. 727-758. (Pubitemid 127571867)
8. Batra, R. C.; Ching, H. K. (2002): Analysis of elastodynamic deformation near a crack/notch tip by the meshless local Petrov-Galerkin (MLPG) Method. CMES: Computer Modeling in Engineering & Sciences, vol. 3, no. pp. 717-730.
9. Belytschko, T.; Guo, Y.; Liu, W. K.; Xiao, S. P. (2000): A unified stability of meshless particle methods. Int. J. Numer. Methods Engrg., vol. 48, no. pp. 1359-1400.
10. Belytschko, T.; Lu, Y. Y.; Gu, L. (1994): Element-free Galerkin methods. Int. J. Numer. Methods Engrg., vol. 37, no. pp. 229-256.
11. Ching, H. K.; Batra, R. C. (2001): Determination of crack tip fields in linear elas-tostatics by the meshless local Petrov-Galerkin (MLPG) method. CMES: Computer Modeling in Engineering & Sciences, vol. 2, no. pp. 273-290.
12. Ching, H. K.; Yen, S. C. (2005): Meshless local Petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads. Composites: Part B, vol. 36, no. pp. 223-240. (Pubitemid 40151901)
13. Ching, H. K.; Yen, S. C. (2006): Transient thermoelastic deformations of 2-D functionally graded beams under nonuniformly convective heat supply. Compos. Struct, vol. 73, no. pp. 381-393. (Pubitemid 43323650)
14. Duarte, C. A.; Oden, J. T. (1996): An h-p adaptive method using clouds. Comput. Methods Appl. Mech. Engrg., vol. 139, no. pp. 237-262. (Pubitemid 126382699)
15. Gilhooley, D. F.; Batra, R. C.; Xiao, J. R.; McCarthy, M. A.; Gillespie Jr., J. W. (2007): Analysis of thick functionally graded plates by using higher-order shear and normal deformable plate theory and MLPG method with radial basis functions. Compos. Struct, vol. 80, no. pp. 539-552. (Pubitemid 46359845)
16. Gu, Y. T.; Liu, G. R. (2001): A meshless local Petrov-Galerkin (MLPG) formulation for static and free vibration analyses of thin plates. CMES: Computer Modeling in Engineering & Sciences, vol. 2, no. pp. 463-476. (Pubitemid 33620143)
17. Gu, Y. T.; Wang, Q. X.; Lam, K. Y.; Dai, K. Y. (2007): A pseudo-elastic local meshless method for analysis of material nonlinear problems in solids. Eng. Anal. Bound. Elem., vol. 31, no. pp. 771-782. (Pubitemid 47189642)
18. Han, Z. D.; Atluri, S. N. (2004): Meshless Local Petrov-Galerkin (MLPG) approaches for solving 3D Problems in elasto-statics. CMES: Computer Modeling in Engineering & Sciences, vol. 6, no. pp. 168-188.
19. Han, Z. D.; Rajendran, A. M.; Atluri, S. N. (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. pp. 1-12. (Pubitemid 43037156)
20. Heaney, C.; Augarde, C.; Deeks, A. (2009): Modelling Elasto-Plasticity Using the Hybrid MLPG Method. CMES: Computer Modeling in Engineering & Sciences, vol. 56, no. 2, pp. 153-178.
21. Kim, H. G.; Atluri, S. N. (2000): Arbitrary placement of secondary nodes, and error control, in the meshless local Petrov-Galerkin (MLPG) method. CMES: Computer Modeling in Engineering & Sciences, vol. 1, no. pp. 11-32.
22. Li, Q.; Soric, J.; Jarak, T.; Atluri, S. N. (2005): A locking-free meshless local Petrov-Galerkin formulation for thick and thin plates. J. Comput. Phys., vol. 208, no. pp. 116-133. (Pubitemid 40714216)
23. Lin, H.; Atluri, S. N. (2000): Meshless local Petrov-Galerkin (MLPG) method for convection-diffusion problems. CMES: Computer Modeling in Engineering & Sciences, vol. 1, no. pp. 45-60.
24. Lin, H.; Atluri, S. N. (2001): The meshless local Petrov-Galerkin (MLPG) method for solving incompressible Navier-Stokes equations. CMES: Computer Modeling in Engineering & Sciences, vol. 2, no. pp. 117-142. (Pubitemid 33626565)
25. Liu, G. R.; Gu, Y. T. (2005): An Introduction to Meshfree Methods and Their Programming. Springer
26. Liu, W. K.; Jun, S.; Zhang, Y. (1995): Reproducing kernel particle methods. Int. J. Numer. Methods in Fluids, vol. 20, no. pp. 1081-1106.
27. Long, S.; Atluri, S. N. (2002): A meshless local Petrov-Galerkin (MLPG) method for solving the bending problem of a thin plate. CMES: Computer Modeling in Engineering & Sciences, vol. 3, no. pp. 53-64.
28. 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. pp. 203-216.
29. Lucy, L. B. (1977): A numerical approach to the testing of the fission hypothesis. Astronom. J., vol. 82, no. pp. 1013-1024.
30. Nayroles, B.; Touzot, G.; Villon, P. (1992): Generalizing the finite element method: diffuse approximation and diffuse elements. Comput. Mech., vol. 10, no. pp. 307-18. (Pubitemid 23570159)
31. Newmark, N. M. (1959): A method of computation for structural dynamics. J. Eng. Mech. Div.-ASCE, vol. 85, no. pp. 67-94.
32. Qian, L. F.; Batra, R. C.; Chen, L. M. (2003): Elastostatic Deformations of a Thick Plate by using a Higher-Order Shear and Normal Deformable Plate Theory and two Meshless Local Petrov-Galerkin (MLPG) Methods. CMES: Computer Modeling in Engineering & Sciences, vol. 4, no. pp. 161-175. (Pubitemid 37360207)
33. Qian, L. F.; Batra, R. C.; Chena, L. M. (2004): Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local Petrov-Galerkin method. Composites: Part B, vol. 35, no. pp. 685-697.
34. Rezaei Mojdehi, A.; Darvizeh, A.; Basti, A. (2011): Application of Meshless Local Petrov-Galerkin (MLPG) Method to Three Dimensional Elasto-Plastic Problems based on Deformation Theory of Plasticity. CMES: Computer Modeling in Engineering & Sciences, vol. 77, no. pp. 1-31.
35. Rezaei Mojdehi, A.; Darvizeh, A.; Basti, A.; Rajabi, H. (2011): Three dimensional static and dynamic analysis of thick functionally graded plates by the mesh-less local Petrov-Galerkin (MLPG) method. Eng. Anal. Bound. Elem., vol. 35, no. pp. 1168-1180.
36. Sladek, J.; Sladek, V.; Atluri, S. N. (2001): A pure contour formulation for the meshless local boundary intergral equation method in thermoelasticity. CMES: Computer Modeling in Engineering & Sciences, vol. 2, no. pp. 423-433. (Pubitemid 33620140)
37. Sladek, J.; Sladek, V.; Krivacek, J.; Wen, P. H.; Zhang, C. h. (2007): Meshless local Petrov-Galerkin (MLPG) method for Reissner-Mindlin plates under dynamic load. Comput. Methods Appl. Mech. Engrg., vol. 196, no. pp. 2681-2691. (Pubitemid 46554975)
38. Sladek, J.; Sladek, V.; Solek, P. (2009): Elastic analysis in 3D anisotropic functionally graded solids by the MLPG. Comput. Methods Appl. Mech. Engrg., vol. 43, no. pp. 223-251.
39. Sladek, J.; sladek, V.; Zhang, C. h. (2005): Stress analysis in anisotropic functionally graded materials by the MLPG method. Eng. Anal. Bound. Elem., vol. 29, no. pp. 597-609. (Pubitemid 40683920)
40. Soares, D.; Sladek, J.; Sladek, V. (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, no. pp. 115-140.
41. Soric, J.; Li, Q.; Jarak, T.; Atluri, S. N. (2004): Meshless Local Petrov-Galerkin (MLPG) Formulation for Analysis of Thick Plates. CMES: Computer Modeling in Engineering & Sciences, vol. 6, no. pp. 349-357.
42. Sukumar, N.; Moran, B.; Belytschko, T. (1998): The natural element method in solid mechanics. Int. J. Numer. Methods Engrg., vol. 43, no. pp. 839-887.
43. Tang, Z.; Shen, S.; Atluri, S. N. (2003): Analysis of materials with strain-gradient effects: A meshless local Petrov-Galerkin (MLPG) approach, with nodal displacements only. CMES: Computer Modeling in Engineering & Sciences, vol. 4, no. pp. 177-196. (Pubitemid 37360208)
44. Wendland, H. (1995): Piecewise polynomial positive definite and compactly supported radial basis functions of minimal degree. Adv. Comput. Methods, vol. 4, no. pp. 389-396. (Pubitemid 126012128)
45. Xiao, J. R.; Batra, R. C.; Gilhooley, D. F.; Gillespie Jr., J. W.; McCarthy, M. (2007): Analysis of thick plates by using a higher-order shear and normal de-formable plate theory and MLPG method with radial basis functions. Comput. Methods Appl. Mech. Engrg., vol. 196, no. pp. 979-987. (Pubitemid 44644877)
46. Zhang, G. M.; Batra, R. C. (2004): Modified smoothed particle hydrodynamics method and its application to transient problems. Comput. Mech., vol. 34, no. pp. 137-46.
47. Zhang, X.; Zhenhan, Y.; Zhangfei, Z. (2006): Application of MLPG in large deformation analysis. Acta Mech. Sin., vol. 22, no. pp. 331-340. (Pubitemid 44678191)