Boundary locking induced by penalty enforcement of essential boundary conditions in mesh-free methods

Computer Methods in Applied Mechanics and Engineering

Volumn 197, Issue 13-16, 2008, Pages 1167-1183

  Cho, Jin Yeon ^a   Song, You Me ^a   Choi, Yun Hyuk ^a  

^a Inha University   (South Korea)

Author keywords

Boundary locking; Essential boundary conditions; Mesh free method; Moving least squares method; Over constraint phenomena; Penalty method; Reproducing kernel particle method

Indexed keywords

BOUNDARY CONDITIONS; LEAST SQUARES APPROXIMATIONS; NUMERICAL METHODS; PROBLEM SOLVING;

BOUNDARY LOCKING; ESSENTIAL BOUNDARY CONDITIONS; MESH-FREE METHODS; MOVING LEAST SQUARES METHOD; PENALTY METHOD; REPRODUCING KERNEL PARTICLE METHOD;

COMPUTER SIMULATION;

BOUNDARY CONDITIONS; COMPUTER SIMULATION; LEAST SQUARES APPROXIMATIONS; NUMERICAL METHODS; PROBLEM SOLVING;

EID: 38349061684     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.09.020     Document Type: Article

References (21)

1. Lucy L.B. A numerical approach to the testing of the fission hypothesis. Astron. J, 82 12 (1977) 1013-1024
2. Liszka T., and Orkisz J. The finite difference method at arbitrary irregular grids and its application in applied mechanics. Comput. Struct. 11 102 (1980) 83-95
3. Nayroles B., Touzot G., and Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Comput. Mech. 10 5 (1992) 307-318
4. Belytschko T., Krongauz Y., Organ D., Fleming M., and Krysl P. Meshless methods: an overview and recent developments. Comput. Methods Appl. Mech. Engrg. 139 1-4 (1996) 3-47
5. Liu W.K., Jun S., and Zhang Y.F. Reproducing kernel particle methods. Int. J. Numer. Methods Fluids 20 8-9 (1995) 1081-1106
6. Babuska I., and Melenk J. The partition of unity method. Int. J. Numer. Methods Engrg. 40 4 (1997) 727-758
7. Duarte C.A., and Oden J.T. An h-p adaptive method using clouds. Comput. Methods Appl. Mech. Engrg. 139 1-4 (1996) 237-262
8. Atluri S.N., and Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput. Mech. 22 2 (1998) 117-127
9. Atluri S.N. The Meshless Local-Petrov-Galerkin Method for Domain & BIE Discretizations (2004), Tech Science Press, Forsyth, GA
10. Cho J.Y., An J.M., Song Y.M., Lee S., and Choi D.W. Coupled analysis of independently modeled finite element substructures by moving least squares displacement welding technique. CMES: Comput. Model. Eng. Sci. 9 1 (2005) 1-17
11. Lancaster P., and Salkauskas K. Surfaces generated by moving least squares methods. Math. Comput. 37 155 (1981) 141-158
12. Atluri S.N., Cho J.Y., and Kim H.G. Analysis of thin beams, using the meshless local Petrov-Galerkin method, with generalized moving least squares interpolations. Comput. Mech. 24 5 (1999) 334-347
13. Zhu T., and Atluri S.N. A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method. Comput. Mech. 21 3 (1998) 211-222
14. S.J. Kim, Y.J. Choi, Analysis of Mindlin plate by the element free Galerkin method applying penalty technique, in: Proceeding of 40th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, St. Louis, MO, 1999, pp. 403-410.
15. Choi Y.J., and Kim S.J. Bending analysis of Mindlin-Reissner plates by the element free Galerkin method with penalty technique. KSME Int. J. 17 1 (2003) 64-76
16. Atluri S.N., Kim H.G., and Cho J.Y. A critical assessment of the truly meshless local Petrov-Galerkin (MLPG), and local boundary integral equation (LBIE) methods. Comput. Mech. 24 5 (1999) 348-372
17. Chen J.S., and Wang H.P. New boundary condition treatment in meshfree computation of contact problems. Comput. Methods Appl. Mech. Engrg. 187 3-4 (2000) 441-468
18. Krongauz Y., and Belytschko T. Enforcement of essential boundary conditions in meshless approximations using finite elements. Comput. Methods Appl. Mech. Engrg. 131 1-2 (1996) 133-145
19. Reddy J.N., and Rasmussen M.L. Advanced Engineering Analysis (1982), John Wiley & Sons, New York
20. Bartle R.G., and Sherbert D.R. Introduction to Real Analysis (1982), John Wiley & Sons, New York
21. Strang G. Linear Algebra and its Applications. second ed. (1980), Academic Press, New York