Avoiding shear locking for the Timoshenko beam problem via isogeometric collocation methods

Computer Methods in Applied Mechanics and Engineering

Volumn 241-244, Issue , 2012, Pages 38-51

  Beirao da Veiga L ^a,b   Lovadina, C ^b,c   Reali, A ^b,c  

^a UNIVERSITY OF MILAN   (Italy)

^b CNR   (Italy)

^c UNIVERSITY OF PAVIA   (Italy)

Author keywords

B splines; Collocation methods; Isogeometric analysis; Timoshenko beam

Indexed keywords

APPROXIMATION DEGREES; B SPLINES; COLLOCATION METHOD; ISOGEOMETRIC ANALYSIS; LOCKING-FREE; MIXED METHOD; NUMERICAL TESTS; SHEAR-LOCKING; THEORETICAL RESULT; TIMOSHENKO BEAMS;

PARTICLE BEAMS;

NUMERICAL METHODS;

EID: 84862994342     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2012.05.020     Document Type: Article

References (25)

1. Akkermann I., Bazilevs Y., Calo V.M., Hughes T.J.R., Hulshoff S. The role of continuity in residual-based variational multiscale modeling of turbulence. Comput. Mech. 2008, 41:371-378.
2. Auricchio F., Beirão da Veiga L., Buffa A., Lovadina C., Reali A., Sangalli G. A fully "locking-free" isogeometric approach for plane linear elasticity problems: a stream function formulation. Comput. Methods Appl. Mech. Engrg. 2007, 197:160-172.
3. Auricchio F., Beirão da Veiga L., Hughes T.J.R., Reali A., Sangalli G. Isogeometric collocation methods. Math. Models Methods Appl. Sci. 2010, 20:2075-2107.
4. F. Auricchio, L. Beirão da Veiga, T.J.R. Hughes, A. Reali, G. Sangalli, Isogeometric collocation for elastostatics and explicit dynamics. Comput. Methods Appl. Mech. Engrg., in press. doi:10.1016/j.cma.2012.03.026.
5. Auricchio F., Beirão da Veiga L., Lovadina C., Reali A. The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: mixed FEMs versus NURBS-based approximations. Comput. Methods Appl. Mech. Engrg. 2010, 199:314-323.
6. F. Auricchio, F. Calabrò, T.J.R. Hughes, A. Reali, G. Sangalli, A simple algorithm for obtaining nearly optimal quadrature rules for NURBS-based isogeometric analysis, Comput. Methods Appl. Mech. Engrg., in press. doi:10.1016/j.cma.2012.04.014.
7. Bazilevs Y., Beirão da Veiga L., Cottrell J.A., Hughes T.J.R., Sangalli G., approximation Isogeometric analysis: stability and error estimates for h-refined meshes. Math. Models Methods Appl. Sci. 2006, 16:1-60.
8. Bazilevs Y., Michler C., Calo V.M., Hughes T.J.R. Weak Dirichlet boundary conditions for wall-bounded turbulent flows. Comput. Methods Appl. Mech. Engrg. 2007, 196:4853-4862.
9. Bazilevs Y., Calo V.M., Cottrell J.A., Hughes T.J.R., Reali A., Scovazzi G. Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput. Methods Appl. Mech. Engrg. 2007, 197:73-201.
10. Beirão da Veiga L., Buffa A., Rivas J., Sangalli G. Some estimates for h-p-k- refinement in isogeometric analysis. Numer. Math. 2011, 118:271-305.
11. Beirão da Veiga L., Buffa A., Lovadina C., Martinelli M., Sangalli G. An isogeometric method for the Reissner-Mindlin plate bending problem. Comput. Methods Appl. Mech. Engrg. 2012, 209-212:45-53.
12. Beirão da Veiga L., Cho D., Sangalli G. Anisotropic NURBS approximation in isogeometric analysis. Comput. Meth. Appl. Mech. Engrg. 2012, 209-212:1-11.
13. Cottrell J.A., Hughes T.J.R., Bazilevs Y. Isogeometric Analysis. Towards integration of CAD and FEA 2009, Wiley.
14. Cottrell J.A., Reali A., Bazilevs Y., Hughes T.J.R. Isogeometric analysis of structural vibrations. Comput. Meth. Appl. Mech. Engrg. 2006, 195:5257-5296.
15. Cottrell J.A., Hughes T.J.R., Reali A. Studies of refinement and continuity in isogeometric structural analysis. Comput. Meth. Appl. Mech. Engrg. 2007, 196:4160-4183.
16. de Boor C. A Practical Guide to Splines 2001, Springer.
17. de Falco C., Reali A., Vázquez R. GeoPDEs: a research tool for IsoGeometric analysis of PDEs. Adv. Engrg. Softw. 2011, 42:1020-1034.
18. Demko S. On the existence of interpolation projectors onto spline spaces. J. Approximat. Theory 1985, 43:151-156.
19. Hughes T.J.R., Cottrell J.A., Bazilevs Y. Isogeometric analysis: CAD finite elements NURBS exact geometry and mesh refinement. Comput. Methods Appl. Mech. Engrg. 2005, 194:4135-4195.
20. Hughes T.J.R., Reali A., Sangalli G. Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with k-method NURBS. Comput. Methods Appl. Mech. Engrg. 2008, 197:4104-4124.
21. Hughes T.J.R., Reali A., Sangalli G. Efficient quadrature for NURBS- based isogeometric analysis. Comput. Methods Appl. Mech. Engrg. 2010, 199:301-313.
22. Johnson R.W. A B-spline collocation method for solving the incompressible Navier-Stokes equations using an ad hoc method: the boundary residual method. Comput. Fluids 2005, 34(1):121-149.
23. Reali A. An isogeometric analysis approach for the study of structural vibrations. J. Earthquake Engrg. 2006, 10:1 1-30.
24. Timoshenko S.P. On the correction factor for shear of the differential equation for transverse vibrations of bars of uniform cross-section. Phil. Mag. 1921, 41:744-746.
25. Zhang Y., Bazilevs Y., Goswami S., Bajaj C.L., Hughes T.J.R. Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow. Comput. Methods Appl. Mech. Engrg. 2007, 196:2943-2959.