Floating stress-point integration meshfree method for large deformation analysis of elastic and elastoplastic materials

International Journal for Numerical Methods in Engineering

Volumn 92, Issue 1, 2012, Pages 36-55

  Onishi, Y ^a   Amaya, K ^a  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Galerkin meshfree method; Incremental equilibrium equation; Large deformation; Moving least squares; Stress point integration; Updated Lagrangian

Indexed keywords

EQUILIBRIUM EQUATION; LAGRANGIAN; LARGE DEFORMATIONS; MESH-FREE METHOD; MOVING LEAST SQUARES;

COMPUTATIONAL MECHANICS; DEFORMATION; ELASTOPLASTICITY; FINITE ELEMENT METHOD; GALERKIN METHODS; LAGRANGE MULTIPLIERS;

INTEGRATION;

EID: 84866446004     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.4321     Document Type: Article

References (32)

1. Li S, Liu WK. Meshfree and particle methods and their applications. Applied Mechanics Reviews 2002; 55(1):1-34.
2. Nguyen VP, Rabczuk T, Bordas S, Duflot M. Meshless methods: a review and computer implementation aspects. Mathematics and Computers in Simulation 2008; 79(3):763-813.
3. SIMULIA Inc. ABAQUS 6.8 Documentation. SIMULIA: Dassault Systemes S.A., Velizy-Villacoublay, FRANCE, 2008.
4. Zienkiewicz OC, Huang GC, Liu YC. Adaptive FEM computation of forming processes - application to porous and non-porous materials. International Journal for Numerical Methods in Engineering 1990; 30:1527-1553.
5. MSC. Software Corp. MARC 2010 Theory and User Information. MSC Software Corporation: Santa Ana, CA, USA, 2010.
6. Cheng JH, Kikuchi N. A mesh re-zoning technique for finite element simulations of metal forming processes. International Journal for Numerical Methods in Engineering 1986; 23:219-228.
7. Belytschko T, Lu YY, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering 1994; 37:229-256.
8. Beissel S, Belytschko T. Nodal integration of the element-free Galerkin method. Computer Methods in Applied Mechanics and Engineering 1996; 139:49-74.
9. Chen JS, Wu CT, Yoon S, You Y. A stabilized conforming nodal integration for Galerkin mesh-free methods. International Journal for Numerical Methods in Engineering 2001; 50:435-466.
10. Chen JS, Yoon S, Wu CT. Non-linear version of stabilized conforming nodal integration for Galerkin mesh-free methods. International Journal for Numerical Methods in Engineering 2002; 53:2587-2615.
11. Sze KY, Chen JS, Sheng N, Liu XH. Stabilized conforming nodal integration: exactness and variational justification. Finite Elements in Analysis and Design 2004; 41:147-171.
12. Puso MA, Chen JS, Zywicz E, Elmer W. Meshfree and finite element nodal integration methods. International Journal for Numerical Methods in Engineering 2008; 74:416-446.
13. Liu GR, Zhang GY, Wang YY, Zhong ZH, Li GY, Han X. A nodal integration technique for meshfree radial point interpolation method (NI-RPIM). International Journal of Solids and Structures 2007; 44:3840-3860.
14. Yaw LL, Sukumar N, Kunnath SK. Meshfree co-rotational formulation for two-dimensional continua. International Journal for Numerical Methods in Engineering 2009; 79:979-1003.
15. Li G, Belytschko T. Element-free Galerkin method for contact problems in metal forming analysis. Engineering Computations 2001; 18(1/2):62-78.
16. Duan Q, Belytschko T. Gradient and dilatational stabilizations for stress-point integration in the element-free Galerkin method. International Journal for Numerical Methods in Engineering 2009; 77:776-798.
17. Randles PW, Libersky LD. Normalized SPH with stress points. International Journal for Numerical Methods in Engineering 2000; 48:1445-1462.
18. Rabczuk T, Belytschko T, Xiao SP. Stable particle methods based on Lagrangian kernels. Computer Methods in Applied Mechanics and Engineering 2004; 193:1035-1063.
19. Felgueroso LC, Colominas I, Mosqueira G, Navarrina F, Casteleiro M. On the Galerkin formulation of the smoothed particle hydrodynamics method. International Journal for Numerical Methods in Engineering 2004; 60:1475-1512.
20. Onishi Y, Amaya K. A novel meshfree method for large deformation analysis of elastic and viscoelastic bodies without using background cells. Journal of Solid Mechanics and Materials Engineering 2010; 4(11):1673-1686.
21. Gurtin ME, Spear K. On the relationship between the logarithmic strain rate and the stretching tensor. International Journal of Solids and Structures 1983; 19(5):437-444.
22. Hoger A. The material time derivative of logarithmic strain. International Journal of Solids and Structures 1986; 22(9):1019-1032.
23. Anand L. A rate constitutive equation for moderate strain isotropic elasticity. Mechanics Research Communications 1984; 11(5):345-352.
24. Schreyer HL, Kulak RF, Kramer JM. Accurate numerical solutions for elastic-plastic models. Journal of Pressure Vessel Technology, Transactions of ASME 1979; 101(3):226-234.
25. ANSYS Inc. GAMBIT 2.4 Documentation. ANSYS Inc.: Canonsburg, PA, USA, 2007.
26. Krongauz Y, Belytschko T. Consistent pseudo-derivatives in meshless methods. Computer Methods in Applied Mechanics and Engineering 1997; 146:371-386.
27. Liu Y, Belytschko T. A new support integration scheme for the weakform in mesh-free methods. International Journal for Numerical Methods in Engineering 2010; 82:699-715.
28. Liu GR. Meshfree Methods, 2nd (edn). CRC Press: Boca Raton, FL, USA, 2010.
29. Jan Y, Sheu TW. A quasi-implicit time advancing scheme for unsteady incompressible flow. Part I: Validation. Computer Methods in Applied Mechanics and Engineering 2007; 196:4755-4770.
30. Murea CM. A semi-implicit algorithm based on the augmented Lagrangian method for fluid-structure interaction. Numerical Mathematics and Advanced Applications, Proceedings of ENUMATH 2007, Graz, AUSTRIA, 2008; 555-562.
31. Zienkiewicz OC. The Finite Element Method for Solid and Structural Mechanics. (6th edn). Elsevier Inc.: Burlington, MA, USA, 2005.
32. Hisada T, Noguchi H. Basis and Application of Non-linear Finite Element Method (in Japanese). Maruzen Company: Tokyo, JAPAN, 1995.