NURBS-based parametric mesh-free methods

Computer Methods in Applied Mechanics and Engineering

Volumn 197, Issue 17-18, 2008, Pages 1541-1567

  Shaw, Amit ^a   Roy, D ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Error reproducing kernels; Geometric map; Interpolations; Mesh free methods; NURBS; Parametric ERKM

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; ERRORS; GEOMETRY; GRID COMPUTING; POLYNOMIALS;

ERROR REPRODUCING KERNEL METHOD (ERKM); NON-UNIFORM-RATIONAL-B-SPLINES (NURBS); PARAMETRIC MESH-FREE METHODS;

COMPUTER SIMULATION;

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; ERRORS; GEOMETRY; GRID COMPUTING; POLYNOMIALS;

EID: 39149086676     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.11.024     Document Type: Article

References (40)

1. Atluri S.N., Kim H.G., and Cho J.Y. A critical assessment of the truly Meshless local Petrov-Galerkin (MLPG) methods. Comput. Mech. 24 (1999) 348-372
2. Babuska I., and Melenk J.M. The partition of unity method. Int. J. Numer. Meth. Engng. 40 (1997) 727-758
3. Belytschko T., Lu Y.Y., and Gu L. Element-free Galerkin methods. Int. J. Numer. Meth. Engng. 37 (1994) 229-256
4. Bazilevs Y., Veiga B., Cottrell J.A., Hughes T.J.R., and Sangalli G. Isogeometric analysis: Approximation, stability and error estimates for h-refined meshes. Math. Meth. Models Appl. Sci. 16 (2006) 1031-1090
5. Y. Bazilevs, V.M. Calo, J.A. Cottrell, T.J.R. Hughes, A. Reali, G. Scovazzi, Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows, Comp. Meth. Appl. Mech. Engng., in press. doi:10.1016/j.cma.2007.07.016.
6. Bazilevs Y., Calo V.M., Zhang Y., and Hughes T.J.R. Isogeometric fluid-structure interaction analysis with applications to arterial blood flow. Comput. Mech. 38 (2006) 310-322
7. Chen J.S., Pan C., Wu T.C., and Liu W.K. Reproducing kernel particle methods for large deformation analysis of non-linear structures. Comp. Meth. Appl. Mech. Engng. 139 (1996) 195-227
8. Chen J.S., Pan C., and Wu T.C. Large deformation analysis of rubber based on a reproducing kernel particle method. Comput. Mech. 19 (1997) 211-227
9. Chessa J., and Belytschko T. A local space-time discontinuous finite element method. Comp. Meth. Appl. Mech. Engng. 195 (2006) 1325-1343
10. Cottrell J.A., Reali A., Bazilevs Y., and Hughes T.J.R. Isogeometric analysis of structural vibrations. Comp. Meth. Appl. Mech. Engng. 195 (2006) 5257-5296
11. Dai K.Y., Liu G.R., Lim K.M., and Gu Y.T. Comparison between the radial point interpolation and the Kriging interpolation used in meshfree methods. Comput. Mech. 32 (2003) 60-70
12. Duarte C.A., and Oden J.T. An h-p adaptive method using clouds. Comp. Meth. Appl. Mech. Engng. 139 (1997) 237-262
13. Gingold R.A., and Monaghan J.J. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society 181 (1977) 275-389
14. Gu Y.T., and Liu G.R. A boundary point interpolation method for stress analysis of solids. Comput. Mech. 28 1 (2001) 47-54
15. Han W., and Meng X. Error analysis of the reproducing kernel particle method. Comput. Methods Appl. Mech. Engrg. 190 (2001) 6157-6181
16. Hughes T.J.R., Cottrell J.A., and Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comp. Meth. Appl. Mech. Engng. 194 (2005) 4135-4195
17. Kitanidis P.K. Introduction to Geostatistics: Applications to Hydrogeology (1997), Cambridge University Press
18. Lam K.Y., Wang Q.X., and Li H. A novel approach - Local Kriging (LoKriging) method with two dimensional structural analysis. Comput. Mech. 33 (2004) 235-244
19. n hierarchies. Comp. Meth. Appl. Mech. Engng. 193 (2004) 953-987
20. Liu G.R., and Gu Y.T. A point interpolation method for two-dimensional solids. Int. J. Numer. Meth. Engng. 50 (2001) 937-951
21. Liu W.K., Han W., Lu H., and Li S. Reproducing kernel element method, part I theoretical formulation. Comp. Meth. Appl. Mech. Engng. 193 (2004) 933-951
22. Liu W.K., Jun S., Li S., Adee J., and Belytschko T. Reproducing kernel particle methods for structural dynamics. Int. J. Numer. Meth. Engng. 38 (1995) 1655-1679
23. Liu W.K., Jun S., and Zhang Y.F. Reproducing kernel particle methods. Int. J. Numer. Meth. Fluid 20 (1995) 1081-1106
24. Liu W.K., Li S., and Belytschko T. Moving least square reproducing kernel methods (I) methodology and convergence. Comp. Meth. Appl. Mech. Engng. 143 (1997) 113-154
25. Lu H., Li S., Simkins D.C., Liu W.K., and Cao J. Reproducing kernel element method part III. Generalized enrichment and applications. Comp. Meth. Appl. Mech. Engng. 193 (2004) 989-1011
26. Lu Y.Y., Belytschko T., and Gu L. A new implementation of the element free Galerkin method. Comp. Meth. Appl. Mech. Engng. 113 (1994) 397-414
27. Miyamura T. Wrinkling on stretched circular membrane under in-plane torsion: Bifurcation analyses and experiments. Engng. Struct. 23 (2000) 1407-1425
28. Melenk J.M., and Babuska I. The partition of unity finite element method: basic theory and applications. Comp. Meth. Appl. Mech. Engng. 139 (1996) 289-314
29. Nayroles B., Touzot G., and Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Comput. Mech. 10 (1992) 307-318
30. Olea R.A. Geostatistics for Engineers and Earth Scientists (1999), Kluwer Academic Publishers, Boston
31. Piegl L., and Tiller W. The NURBS Book (1995), Springer, Berlin
32. Roddeman D.G., Drukker J., Oomens C.W.J., and Janssen J.D. The wrinkling of thin membranes: Part I - theory; Part II - numerical analysis. J. Appl. Mech. (ASME) 54 (1987) 884-892
33. Shaw A., and Roy D. Improved procedure for static and dynamic analysis of wrinkled membranes. J. Appl. Mech. (ASME) 74 3 (2007) 590-594
34. Shaw A., and Roy D. A NURBS-based error reproducing kernel method with applications in solid mechanics. Comput. Mech. 40 1 (2007) 127-148
35. Shaw A., and Roy D. Analyses of wrinkled and slack membranes through an error reproducing mesh-free method. Int. J. Solid Struct 44 11-12 (2007) 3939-3972
36. A. Shaw, S. Bendapudi, D. Roy, A Kriging-based error reproducing and interpolating kernel method for improved mesh-free approximations, Int. J. Numer. Meth. Engng., in press. doi:10.1002/nme.2127.
37. n(n ≥ 1) triangular hierarchy. Comp. Meth. Appl. Mech. Engng. 193 (2004) 1013-1034
38. Swegle J.W. Smoothed particle hydrodynamics stability analysis. J. Comput. Phys. 116 (1995) 123-134
39. Zhang Y., Bazilevs Y., Goswami S., Bajaj C., and Hughes T.J.R. Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow. Comp. Meth. Appl. Mech. Engng. 196 (2007) 2943-2959
40. Zhu T., Zhang J., and Atluri S.N. A meshless local boundary integral equation (LBIE) method for solving nonlinear problems. Comput. Mech. 22 (1998) 174-186