Isogeometric analysis using T-splines

Computer Methods in Applied Mechanics and Engineering - Tập 199 Số 5-8 - Trang 229-263 - 2010
Yuri Bazilevs1, Victor M. Calo2, J. Austin Cottrell3, John A. Evans3, Thomas J.R. Hughes3, S. Lipton3, Michael A. Scott3, Thomas W. Sederberg4
1Department of Structural Engineering, University of California, San Diego, 9500 Gilman Drive, Mail Code 0085, La Jolla, CA 92093, USA
2King Abdullah University of Science & Technology
3Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th Street, 1 University Station C0200, Austin, TX 78712, USA
4BRIGHAM YOUNG UNIV

Tóm tắt

Từ khóa


Tài liệu tham khảo

1999

Akkerman, 2008, The role of continuity in residual-based variational multiscale modeling of turbulence, Comput. Mech., 41, 371, 10.1007/s00466-007-0193-7

Auricchio, 2007, A fully “locking-free” isogeometric approach for plane linear elasticity problems: a stream function formulation, Comput. Methods Appl. Mech. Engrg., 197, 160, 10.1016/j.cma.2007.07.005

Bazilevs, 2006, Isogeometric analysis: approximation, stability and error estimates for h-refined meshes, Math. Models Methods Appl. Sci., 16, 1031, 10.1142/S0218202506001455

Bazilevs, 2007, Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows, Comput. Methods Appl. Mech. Engrg., 197, 173, 10.1016/j.cma.2007.07.016

Bazilevs, 2008, Isogeometric fluid–structure interaction: theory, algorithms, and computations, Comput. Mech., 43, 3, 10.1007/s00466-008-0315-x

Bazilevs, 2006, Isogeometric fluid–structure interaction analysis with applications to arterial blood flow, Comput. Mech., 38, 310, 10.1007/s00466-006-0084-3

Bazilevs, 2008, NURBS-based isogeometric analysis for the computation of flows about rotating components, Comput. Mech., 43, 143, 10.1007/s00466-008-0277-z

Y. Bazilevs, C. Michler, V.M. Calo, T.J.R. Hughes, Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes, Comput. Methods Appl. Mech. Engrg., doi:10.1016/j.cma.2008.11.020.

Belytschko, 1985, Stress projection for membrane and shear locking in shell finite elements, Comput. Methods Appl. Mech. Engrg., 51, 221, 10.1016/0045-7825(85)90035-0

Brooks, 1982, Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations, Comput. Methods Appl. Mech. Engrg., 32, 199, 10.1016/0045-7825(82)90071-8

S.B. Brunnermeier, S.A. Martin, Interoperability cost analysis of the US automotive supply chain, National Institute of Standards and Technology, NIST Planning Report 99-1, 1999.

Calo, 2008, Multiphysics model for blood flow and drug transport with applications to patient-specific coronary artery flow, Comput. Mech., 43, 161, 10.1007/s00466-008-0321-z

Catmull, 1978, Recursively generated B-spline surfaces on arbitrary topological meshes, Comput. Aided Des., 10, 350, 10.1016/0010-4485(78)90110-0

Cirak, 2001, Fully C1-conforming subdivision elements for finite deformation thin shell analysis, Int. J. Numer. Methods Engrg., 51, 813, 10.1002/nme.182.abs

Cirak, 2000, Subdivision surfaces: a new paradigm for thin shell analysis, Int. J. Numer. Methods Engrg., 47, 2039, 10.1002/(SICI)1097-0207(20000430)47:12<2039::AID-NME872>3.0.CO;2-1

Cirak, 2002, Integrated modeling, finite-element analysis, and engineering design for thin-shell structures using subdivision, Comput. Aided Des., 34, 137, 10.1016/S0010-4485(01)00061-6

Cottrell, 2007, Studies of refinement and continuity in isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 196, 4160, 10.1016/j.cma.2007.04.007

Cottrell, 2006, Isogeometric analysis of structural vibrations, Comput. Methods Appl. Mech. Engrg., 195, 5257, 10.1016/j.cma.2005.09.027

M. Dorfel, B. Juttler, B. Simeon, Adaptive isogeometric analysis by local h-refinement with T-splines, Comput. Methods Appl. Mech. Engrg., this issue.

Elguedj, 2008, B¯ and F¯ projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements, Comput. Methods Appl. Mech. Engrg., 197, 2732, 10.1016/j.cma.2008.01.012

Evans, 2009, N-widths, sup–infs, and optimality ratios for the k-version of the isogeometric finite element method, Comput. Methods Appl. Mech. Engrg., 198, 1726, 10.1016/j.cma.2009.01.021

Farin, 1999

Farin, 1999

C.A. Felippa, Course notes for advanced finite element methods. <http://caswww.colorado.edu/Felippa.d/FelippaHome.d/Home.html>.

T. Finnigan, Arbitrary degree T-splines, Master’s thesis, Department of Computer Science, Brigham Young University, 2008.

Gomez, 2008, Isogeometric analysis of the Cahn–Hilliard phase-field model, Comput. Methods Appl. Mech. Engrg., 197, 4333, 10.1016/j.cma.2008.05.003

Hoschek, 1993

Hughes, 2000

Hughes, 2005, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement, Comput. Methods Appl. Mech. Engrg., 194, 4135, 10.1016/j.cma.2004.10.008

Hughes, 1988, A mixed finite element formulation for Reissner–Mindlin plate theory: uniform convergence of all higher order spaces, Comput. Methods Appl. Mech. Engrg., 67, 223, 10.1016/0045-7825(88)90127-2

Hughes, 2008, 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., 197, 4104, 10.1016/j.cma.2008.04.006

T.J.R. Hughes, A. Realli, G. Sangalli, Efficient quadrature for NURBS-based isogeometric analysis, Comput. Methods Appl. Mech. Engrg., this issue.

Kasik, 2005, Ten CAD model challenges, IEEE Comput. Graph. Appl., 25, 10.1109/MCG.2005.48

X. Li, X. Guo, H. Wang, Y. He, X. Gu, H. Qin, Harmonic volumetric mapping for solid modeling applications, in: Proceedings of the 2007 ACM Symposium on Solid and Physical Modeling, Beijing China, 2007.

Lorentz, 1986

Piegl, 1997, 10.1007/978-3-642-59223-2

Prautzsch, 2002

Rank, 2005, High order finite elements for shells, Comput. Methods Appl. Mech. Engrg., 194, 2494, 10.1016/j.cma.2004.07.042

Rogers, 2001

Sederberg, 1984, Implicit representation of parametric curves and surfaces, Comput. Vis. Graph. Image Process., 28, 72, 10.1016/0734-189X(84)90140-3

Sederberg, 2004, T-spline simplification and local refinement, ACM Trans. Graph., 23, 276, 10.1145/1015706.1015715

Sederberg, 2008, Watertight trimmed NURBS, ACM Trans. Graph., 27, 10.1145/1360612.1360678

Sederberg, 2003, T-splines and T-NURCCSs, ACM Trans. Graph., 22, 477, 10.1145/882262.882295

T-Splines, Inc. <http://www.tsplines.com/maya/>.

T-Splines, Inc. <http://www.tsplines.com/rhino/>.

Thurston, 1982, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Am. Math. Soc. (New Series), 6, 357, 10.1090/S0273-0979-1982-15003-0

Thurston, 1997, vol. 1

Wall, 2008, Isogeometric structural shape optimization, Comput. Methods Appl. Mech. Engrg., 197, 2976, 10.1016/j.cma.2008.01.025

Wang, 2008, Polycube splines, Comput. Aided Des., 40, 721, 10.1016/j.cad.2008.01.012

Warren, 2002

Zhang, 2007, Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow, Comput. Methods Appl. Mech. Engrg., 196, 2943, 10.1016/j.cma.2007.02.009