Isogeometric analysis of 2D gradient elasticity

Computational Mechanics

Volumn 47, Issue 3, 2011, Pages 325-334

  Fischer, Paul ^b   Klassen, Markus ^a   Mergheim, Julia ^b   Steinmann, Paul ^b   Müller, Ralf ^a  

^a France   (Germany)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

Gradient elasticity; Isogeometric analysis

Indexed keywords

DIFFERENTIAL EQUATIONS; ELASTICITY; ELASTOHYDRODYNAMICS; INTERPOLATION; NUMERICAL METHODS; STRAIN ENERGY;

CONVERGENCE BEHAVIORS; DISPLACEMENT-BASED; GOVERNING DIFFERENTIAL EQUATIONS; GRADIENT ELASTICITY; INTERPOLATION SCHEMES; ISOGEOMETRIC ANALYSIS; NUMERICAL APPROACHES; TWO-DIMENSIONAL PROBLEM;

FINITE ELEMENT METHOD;

EID: 79954580534     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-010-0543-8     Document Type: Article

References (29)

1. RD Mindlin 1964 Micro-structure in linear elasticity Arch Ration Mechan Anal 16 1 51 78 160356 0119.40302
2. AC Eringen ES Suhubi 1964 Nonlinear theory of simple microelastic solid-I Int J Eng Sci 2 2 189 203 169423 0138.21202 10.1016/0020-7225(64)90004-7
3. RA Toupin 1962 Elastic materials with couple stresses Arch Ration Mech Anal 11 385 414 144512 0112.16805 10.1007/BF00253945
4. SB Altan EC Aifantis 1992 On the structure of the mode-III crack-tip in gradient elasticity Scr Metall 26 319 324 10.1016/0956-716X(92)90194-J (Pubitemid 23642730)
5. Aifantis EC (1996) Higher order gradients and size effects. In: Carpinteri A (ed) Size-scale effects in the failure mechanisms of materials and structures. Chapman & Hall, London
6. EC Aifantis 1999 Strain gradient interpretation of size effects Int J Fract 95 299 314 10.1023/A:1018625006804 (Pubitemid 30511991)
7. HT Zhu HM Zbib EC Aifantis 1997 Strain gradients and continuum modeling of size effect in metal matrix composites Acta Mech 121 165 176 0885.73044 10.1007/BF01262530 (Pubitemid 127544502)
8. A Zervos SA Papanicolopulos I Vardoulakis 2009 Two finite-element discretizations for gradient elasticity J Eng Mech 13 3 203 213 10.1061/(ASCE)0733-9399(2009)135:3(203)
9. 1 finite element for gradient elasticity Int J Numer Methods Eng 77 1396 1415 2498909 1156.74382 10.1002/nme.2449
10. 1 continuous discretization of nonlinear gradient elasticity: a comparison of NEM and FEM based on Bernstein-Bézier patches Int J Numer Methods Eng 82 1282 1307 2642220 1188.74055
11. H Askes EC Aifantis 2002 Numerical modeling of size effects with gradient elasticity-formulation, meshless discretization and examples Int J Fract 117 347 358 10.1023/A:1022225526483 (Pubitemid 36360802)
12. 1 discretizations for the application to gradient elasticity. In: Maugin G, Metrikine A (eds) Mechanics of generalized continua. Springer, New York, pp 1-2
13. TJR Hughes JA Cottrell Y Bazilevs 2005 Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement Comput Methods Appl Mech Eng 194 4135 4195 2152382 1151.74419 10.1016/j.cma.2004.10.008 (Pubitemid 40875970)
14. Y Bazilevs L Barãoda Veiga JA Cottrell TJR Hughes G Sangalli 2005 Isogeometric analysis: approximation, stability and error estimates for h-refined meshes Math Models Methods Appl Sci 16 7 1031 1090 10.1142/S0218202506001455
15. J Cottrell A Reali Y Bazilevs TJR Hughes 2005 Isogeometric analysis of structural vibrations Comput Methods Appl Mech Eng 195 5257 5296 2243311 10.1016/j.cma.2005.09.027 (Pubitemid 44172039)
16. Y Bazilevs VM Calo Y Zhang TJR Hughes 2006 Isogeometric fluid-structure interaction analysis with applications to arterial blood flow Comput Mech 38 310 322 2246128 1161.74020 10.1007/s00466-006-0084-3 (Pubitemid 43970670)
17. Y Zhang Y Bazilevs S Goswami CL Bajaj TJR Hughes 2005 Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow Comput Methods Appl Mech Eng 196 2943 2959 2325400 10.1016/j.cma.2007.02.009
18. H Gómez VM Calo Y Bazilevs TJR Hughes 2008 Isogeometric analysis of the Cahn-Hilliard phase-field model Comput Methods Appl Mech Eng 197 4333 4352 1194.74524 10.1016/j.cma.2008.05.003
19. F Auricchio L Beirao da Veiga A Buffa C Lovadina A Reali G Sangalli 2007 A fully "locking-free" isogeometric approach for plane linear elasticity problems: a steam function formulation Comupt Methods Appl Mech Eng 197 160 172 2361474 1169.74643 10.1016/j.cma.2007.07.005 (Pubitemid 47570889)
20. F Auricchio L Beirao da Veiga C Lovadina A Reali 2010 The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: mixed FEM versus NURBS-based approximations Comput Methods Appl Mech Eng 199 314 323 2576764 10.1016/j.cma.2008.06.004
21. Cox MG (1971) The numerical evaluation of B-splines. Technical report, National Physics Laboratory, DNAC 4
22. C De Boor 1972 On calculation with B-splines J Approx Theory 6 50 62 338617 0239.41006 10.1016/0021-9045(72)90080-9
23. Piegl L, Tiller W (1997) The NURBS book, 2nd edn. Springer, Berlin
24. J Kiendl K-U Bletzinger J Linhard R Wüchner 2009 Isogeometric shell analysis with Kirchhoff-Love elements Comput Methods Appl Mech Eng 198 3902 3914 10.1016/j.cma.2009.08.013
25. DCC Lam F Yang ACM Chong J Wang P Tong 2003 Experiments and theory in strain gradient elasticity J Mech Phys Solids 51 1477 1508 1077.74517 10.1016/S0022-5096(03)00053-X
26. 1 continuous discretization methods. PAMM (submitted)
27. Reif U (1993) Neue Aspekte in der Theorie der Freiformflächen beliebiger Topologie. PhD-Thesis, University of Stuttgart
28. H Prautzsch 1997 Freeform splines Comput Aided Geom Des 14 201 206 1441190 0906.68158 10.1016/S0167-8396(96)00029-5 (Pubitemid 127403695)
29. J Kiendl Y Bazilevs M-C Hsu R Wüchner K-U Bletzinger 2010 The bending strip method for isogeometric analysis of Kirchhoff-Love shell structures comprised of multiple patches Comput Methods Appl Mech Eng 199 2403 2416 10.1016/j.cma.2010.03.029