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Isogeometric collocation mixed methods for rods
1. | Dipartimento di Ingegneria Civile e Architettura, Università di Pavia, Via Ferrata 3, 27100 Pavia, Italy, Italy |
2. | Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via Cozzi 53, 20125 Milano, Italy |
3. | Institute of Applied Mechanics, TU Braunschweig, Bienroder Weg 87, 38106 Braunschweig, Germany |
4. | Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy |
References:
[1] |
K. Arunakirinathar and B. D. Reddy, Mixed finite element methods for elastic rods of arbitrary geometry, Numerische Mathematik, 64 (1993), 13-43.
doi: 10.1007/BF01388679. |
[2] |
F. Auricchio, L. Beirão da Veiga, T. J. R. Hughes, A. Reali and G. Sangalli, Isogeometric collocation methods, Mathematical Models and Methods in Applied Sciences, 20 (2010), 2075-2107.
doi: 10.1142/S0218202510004878. |
[3] |
F. Auricchio, L. Beirão da Veiga, T. J. R. Hughes, A. Reali and G. Sangalli, Isogeometric collocation for elastostatics and explicit dynamics, Computer Methods in Applied Mechanics and Engineering, 249 (2012), 2-14.
doi: 10.1016/j.cma.2012.03.026. |
[4] |
F. Auricchio, L. Beirão da Veiga, J. Kiendl, C. Lovadina and A. Reali, Locking-free isogeometric collocation methods for spatial Timoshenko rods, Comput. Methods Appl. Mech. Engrg., 263 (2013), 113-126.
doi: 10.1016/j.cma.2013.03.009. |
[5] |
L. Beirão da Veiga, A. Buffa, J. Rivas and G. Sangalli, Some estimates for $h-p-k-$refinement in isogeometric analysis, Numerische Mathematik, 118 (2011), 271-305.
doi: 10.1007/s00211-010-0338-z. |
[6] |
L. Beirão da Veiga, C. Lovadina and A. Reali, Avoiding shear locking for the Timoshenko beam problem via isogeometric collocation methods, Computer Methods in Applied Mechanics and Engineering, 241/244 (2012), 38-51.
doi: 10.1016/j.cma.2012.05.020. |
[7] |
D. Chapelle, A locking-free approximation of curved rods by straight beam elements, Numerische Mathematik, 77 (1997), 299-322.
doi: 10.1007/s002110050288. |
[8] |
J. A. Cottrell, T. J. R. Hughes and Y. Bazilevs, Isogeometric Analysis. Towards Integration of CAD and FEA, Wiley, 2009. |
[9] |
J. A. Cottrell, A. Reali, Y. Bazilevs and T. J. R. Hughes, Isogeometric analysis of structural vibrations, Computer Methods in Applied Mechanics and Engineering, 195 (2006), 5257-5296.
doi: 10.1016/j.cma.2005.09.027. |
[10] | |
[11] |
S. Demko, On the existence of interpolation projectors onto spline spaces, Journal of Approximation Theory, 43 (1985), 151-156.
doi: 10.1016/0021-9045(85)90123-6. |
[12] |
T. J. R. Hughes, J. A. Cottrell and Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement, Computer Methods in Applied Mechanics and Engineering, 194 (2005), 4135-4195.
doi: 10.1016/j.cma.2004.10.008. |
[13] |
T. J. R. Hughes, A. Reali and G. Sangalli, Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: Comparison of $p$-method finite elements with $k$-method NURBS, Computer Methods in Applied Mechanics and Engineering, 197 (2008), 4104-4124.
doi: 10.1016/j.cma.2008.04.006. |
[14] |
R. W. Johnson, A B-spline collocation method for solving the incompressible Navier-Stokes equations using an ad hoc method: The Boundary Residual method, Computers & Fluids, 34 (2005), 121-149.
doi: 10.1016/j.compfluid.2004.03.005. |
[15] |
A. Reali, An isogeometric analysis approach for the study of structural vibrations, Journal of Earthquake Engineering, 10 (2006), 1-30. |
[16] |
D. Schillinger, J. A. Evans, A. Reali, M. A. Scott and T. J. R. Hughes, Isogeometric collocation methods: Cost comparison with Galerkin methods and extension to hierarchical discretizations, Computer Methods in Applied Mechanics and Engineering, 267 (2013), 170-232. |
show all references
References:
[1] |
K. Arunakirinathar and B. D. Reddy, Mixed finite element methods for elastic rods of arbitrary geometry, Numerische Mathematik, 64 (1993), 13-43.
doi: 10.1007/BF01388679. |
[2] |
F. Auricchio, L. Beirão da Veiga, T. J. R. Hughes, A. Reali and G. Sangalli, Isogeometric collocation methods, Mathematical Models and Methods in Applied Sciences, 20 (2010), 2075-2107.
doi: 10.1142/S0218202510004878. |
[3] |
F. Auricchio, L. Beirão da Veiga, T. J. R. Hughes, A. Reali and G. Sangalli, Isogeometric collocation for elastostatics and explicit dynamics, Computer Methods in Applied Mechanics and Engineering, 249 (2012), 2-14.
doi: 10.1016/j.cma.2012.03.026. |
[4] |
F. Auricchio, L. Beirão da Veiga, J. Kiendl, C. Lovadina and A. Reali, Locking-free isogeometric collocation methods for spatial Timoshenko rods, Comput. Methods Appl. Mech. Engrg., 263 (2013), 113-126.
doi: 10.1016/j.cma.2013.03.009. |
[5] |
L. Beirão da Veiga, A. Buffa, J. Rivas and G. Sangalli, Some estimates for $h-p-k-$refinement in isogeometric analysis, Numerische Mathematik, 118 (2011), 271-305.
doi: 10.1007/s00211-010-0338-z. |
[6] |
L. Beirão da Veiga, C. Lovadina and A. Reali, Avoiding shear locking for the Timoshenko beam problem via isogeometric collocation methods, Computer Methods in Applied Mechanics and Engineering, 241/244 (2012), 38-51.
doi: 10.1016/j.cma.2012.05.020. |
[7] |
D. Chapelle, A locking-free approximation of curved rods by straight beam elements, Numerische Mathematik, 77 (1997), 299-322.
doi: 10.1007/s002110050288. |
[8] |
J. A. Cottrell, T. J. R. Hughes and Y. Bazilevs, Isogeometric Analysis. Towards Integration of CAD and FEA, Wiley, 2009. |
[9] |
J. A. Cottrell, A. Reali, Y. Bazilevs and T. J. R. Hughes, Isogeometric analysis of structural vibrations, Computer Methods in Applied Mechanics and Engineering, 195 (2006), 5257-5296.
doi: 10.1016/j.cma.2005.09.027. |
[10] | |
[11] |
S. Demko, On the existence of interpolation projectors onto spline spaces, Journal of Approximation Theory, 43 (1985), 151-156.
doi: 10.1016/0021-9045(85)90123-6. |
[12] |
T. J. R. Hughes, J. A. Cottrell and Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement, Computer Methods in Applied Mechanics and Engineering, 194 (2005), 4135-4195.
doi: 10.1016/j.cma.2004.10.008. |
[13] |
T. J. R. Hughes, A. Reali and G. Sangalli, Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: Comparison of $p$-method finite elements with $k$-method NURBS, Computer Methods in Applied Mechanics and Engineering, 197 (2008), 4104-4124.
doi: 10.1016/j.cma.2008.04.006. |
[14] |
R. W. Johnson, A B-spline collocation method for solving the incompressible Navier-Stokes equations using an ad hoc method: The Boundary Residual method, Computers & Fluids, 34 (2005), 121-149.
doi: 10.1016/j.compfluid.2004.03.005. |
[15] |
A. Reali, An isogeometric analysis approach for the study of structural vibrations, Journal of Earthquake Engineering, 10 (2006), 1-30. |
[16] |
D. Schillinger, J. A. Evans, A. Reali, M. A. Scott and T. J. R. Hughes, Isogeometric collocation methods: Cost comparison with Galerkin methods and extension to hierarchical discretizations, Computer Methods in Applied Mechanics and Engineering, 267 (2013), 170-232. |
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