The least-squares meshfree method for solving linear elastic problems

Computational Mechanics

Volumn 30, Issue 3, 2003, Pages 196-211

  Kwon, K C ^a   Park, S H ^a   Jiang, B N ^b   Youn, S K ^a  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

^b OAKLAND UNIVERSITY   (United States)

Author keywords

Incompressible locking; Integration error; Least squares; Linear elasticity; Meshfree method

Indexed keywords

COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; INTEGRATION; LEAST SQUARES APPROXIMATIONS;

LINEAR ELASTICITY;

ELASTICITY;

EID: 0037296353     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-002-0379-y     Document Type: Article

References (24)

1. Atluri SN, Zhu T (1998) A new meshless Petrov-Galerkin (MLPG) approach in computational mechanics. Comput. Mech. 22: 117-127
2. Beissel S, Belytschko T (1996) Nodal integration of the element-free Galerkin method. Comp. Meth. Appl. Mech. Eng. 139: 49-74
3. Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin methods. Int. J. Num. Meth. Eng. 37: 229-256
4. Breitkopf P, Touzot G, Villon P (2000) Double grid diffuse collocation method. Comput. Mech. 25: 199-206
5. Cai Z, Manteuffel TA, McCormick SF (1997) First-order system least squares for the Stokes equations, with application to linear elasticity. SIAM. J. Numer. Anal. 34: 1727-1741
6. Cai Z, Manteuffel TA, McCormick SF, Parter SV (1998) First-order system least squares (FOSLS) for planar linear elasticity: pure traction problem. SIAM. J. Numer. Anal. 35: 320-335
7. Cai Z, Lee CO, Manteuffel TA, McCormick SF (2000a) First-order system least squares for the Stokes and linear elasticity: numerical results. SIAM. J. Sci. Comput. 5: 1706-1727
8. Cai Z, Lee CO, Manteuffel TA, McCormick SF (2000b) First-order system least squares for the Stokes and linear elasticity equations: further results. SIAM. J. Sci. Comput. 5: 1728-1739
9. Chen JS, Yoon S, Wang HP, Liu WK (2000a) An improved reproducing kernel particle method for nearly incompressible finite elasticity. Comp. Meth. Appl. Mech. Eng. 181: 117-145
10. Chen JS, Wang HP, Yoon S, You Y (2000b) Some recent improvement in meshfree methods for incompressible finite elasticity boundary value problems with contact. Comput. Mech. 25: 137-156
11. Chen JS, Wu CT, Yoon S, You Y (2001) A stabilized conforming nodal integration for Galerkin mesh-free methods. Int. J. Num. Meth. Eng. 50: 435-466
12. De S, Bathe K-J (2001) Displacement/pressure mixed interpolation in the method of finite spheres. Int. J. Num. Meth. Eng. 51: 275-292
13. Dolbow J, Belytschko T (1999) Volumetric locking in the element free Galerkin method. Int. J. Num. Meth. Eng. 46: 925-942
14. Duarte CA, Oden JT (1995) Hp clouds - a meshless method to solve boundary value problems, Technical Report 95-05, TI-CAM, University of Texas at Austin
15. Jiang BN (1998) The Least-Squares Finite Element Method Theory and Application. Springer-Verlag, Berlin
16. Lancaster P, Salkauskas K (1981) Surfaces generated by moving least-squares methods. Math. Comput. 37: 141-158
17. Liu WK, Jun S, Zhang YF (1995) Reproducing kernel particle methods. Int. J. Num. Meth. Fluids. 20: 1081-1106
18. Melenk JM, Babuska I (1996) The partition of unity finite element method: basic theory and applications. Comp. Meth. Appl. Mech. Eng. 139: 289-314
19. Nagashima T (1999) Node-by-node meshless approach and its applications to structural analysis. Int. J. Num. Meth. Eng. 39: 341-385
20. Nayroles B, Touzot G, Villon P (1992) Generalizing the finite element method: diffuse approximation and diffuse elements. Comput. Mech. 10: 307-318
21. Oñate E, Zienkiewicz OC, Taylor RL (1996) A finite point method in computational mechanics. Applications to convective transport and fluid flow. Int. J. Num. Meth. Eng. 39: 3839-3866
22. Park SH, Youn SK (2001) The least-squares meshfree method. Int. J. Num. Meth. Eng. 52: 997-1012
23. Park SH, Kwon KG, Youn SK (2002) A study on the convergence of least-squares meshfree method under inaccurate integration. Int. J. Num. Meth. Eng. in printing
24. Timoshenko SP, Goodier JN (1987) Theory of Elasticity, 3rd edn. McGraw-Hill, New York