A cell-based smoothed radial point interpolation method (CS-RPIM) for static and free vibration of solids

Engineering Analysis with Boundary Elements

Volumn 34, Issue 2, 2010, Pages 144-157

  Cui, X Y ^a,b   Liu, G R ^b,c   Li, G Y ^a  

^a HUNAN UNIVERSITY   (China)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^c SINGAPORE MIT ALLIANCE   (Singapore)

Author keywords

Gradient smoothing operation; Meshfree method; Numerical method; Radial point interpolation method (RPIM); Subdomain stabilized conforming integration

Indexed keywords

CELL-BASED; DISPLACEMENT FIELD; ESSENTIAL BOUNDARY CONDITIONS; FREE VIBRATION; FREE-VIBRATION ANALYSIS; GALERKIN; GENERALIZED GRADIENTS; GRADIENT SMOOTHING OPERATION; KRONECKER DELTA FUNCTIONS; MESHFREE METHOD; NODE SELECTION; NUMERICAL EXAMPLE; PROBLEM DOMAIN; RADIAL POINT INTERPOLATION METHOD; RADIAL POINT INTERPOLATION METHOD (RPIM); SHAPE FUNCTIONS; SMOOTHING OPERATION; SOLUTION PROPERTY; SUBDOMAIN STABILIZED CONFORMING INTEGRATION; SYSTEM EQUATIONS; WEAK FORM;

BOUNDARY ELEMENT METHOD; CELLS; COMPUTATIONAL MECHANICS; CONVERGENCE OF NUMERICAL METHODS; FUNCTION EVALUATION; GALERKIN METHODS; INTERPOLATION; VIBRATION ANALYSIS;

NUMBER THEORY;

EID: 70350755592     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2009.07.011     Document Type: Article

References (25)

1. Monaghan J.J. An Introduction of SPH. Computer Physics Communications 48 (1982) 89-96
2. Nayroles B., Touzot G., and Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Computational Mechanics 10 5 (1992) 307-318
3. Belytschko T., Lu Y.Y., and Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering 37 2 (1994) 229-256
4. Liu W.K., Jun S., and Zhang Y.F. Reproducing kernel particle methods. International Journal for Numerical Methods in Engineering 20 (1995) 1081-1106
5. Onate Idelsohn E.S., Zienkiewicz O.C., and Tylor R.L. A finite point method in computational mechanics, applications to convective transport and fluid flow. International Journal for Numerical Methods in Engineering 39 (1996) 3839-3866
6. Duarte C.A., and Oden J.T. An h-p adaptive methods using clouds. Computer Methods in Applied Mechanics and Engineering 139 (1996) 237-262
7. Atluri S.N., and Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Computational Mechanics 22 2 (1998) 117-127
8. Liu G.R., and Gu Y.T. A point interpolation method for two-dimensional solids. International Journal for Numerical Methods in Engineering 50 (2001) 937-951
9. Wang J.G., and Liu G.R. A point interpolation meshless method based on radial basis functions. International Journal for Numerical Methods in Engineering 54 (2002) 1623-1648
10. Liu G.R. Meshfree methods: moving beyond the finite element method. 2nd ed. (2009), Boca Raton, USA, CRC Press
11. Beissel S., and Belytschko T. Nodal integration of the element-free Galerkin method. Computer Methods in Applied Mechanics and Engineering 139 (1996) 49-74
12. Bonet J., and Kulasegaram S. Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulation. International Journal for Numerical Methods in Engineering 47 (1999) 1189-1214
13. Chen J.S., Wu C.T., Yoon S., and You Y. A stabilized conforming nodal integration for Galerkin meshfree methods. International Journal for Numerical Methods in Engineering 50 (2001) 435-466
14. Liu G.R. A generalized gradient smoothing technique and smoothed bilinear form for Galerkin formulation of a wide class of computational methods. International Journal of Computational Methods 5 2 (2008) 199-236
15. Zhang G.Y., Liu G.R., Nguyen T.T., Song C.X., Han X., Zhong Z.H., et al. The upper boundary property for solid mechanics of linearly conforming radial point interpolation method (LC-RPIM). International Journal of Computational Methods 4 3 (2007) 521-541
16. Liu G.R., and Zhang G.Y. Edge-based smoothed point interpolation methods. International Journal of Computational Methods 5 4 (2008) 621-646
17. Liu G.R., Nguyen T.T., Dai K.Y., and Lam K.Y. Theoretical aspects of the smoothed finite element method (SFEM). International Journal for Numerical Methods in Engineering 71 (2007) 902-930
18. Liu G.R., and Zhang G.Y. A normed G space and weakened weak (W2) formulation of a cell-based smoothed point interpolation method. International Journal of Computational Methods 6 (2009) 147-179
19. Hardy R.L. Theory and applications of the multiquadrics-biharmonic method (20 years of discovery 1968-1988). Computers and Mathematics with Applications 19 (1990) 163-208
20. Golberg M.A., Chen C.S., and Bowman H. Some recent results and proposals for the use of radial basis functions in the BEM. Engineering Analysis with Boundary Elements 23 (1999) 285-296
21. Liu GR. A weakened weak (W2) form for a unified formulation of compatible and incompatible methods, Part I: Theory and Part II: Applications to solid mechanics problems. International Journal for Numerical Methods in Engineering, 2009, doi:10.1002/nme.2719.
22. Wang J.G., and Liu G.R. On The optimal shape parameters of radial basis functions used for 2-D meshless methods. Computer Methods in applied Mechanics and Engineering 191 (2006) 2611-2630
23. Zienkiewicz O.C., and Taylor R.L. The finite element method. 5th ed. (V1: The basis) (2000), Butterworth-Heinemann, Oxford
24. Timoshenko S.P., and Goodier J.N. Theory of elasticity. 3rd ed. (1970), New York, McGraw-Hill
25. Nagashima T. Node-by-node meshless approach and its application to structural analysis. International Journal for Numerical Methods in Engineering 46 (1999) 341-385