,
, Knot vector and B-Spline basis functions
,
,
,
, 10 1.1.4 B-Spline basis function renement, p.12
,
, B-Splines and NURBS: the local renement issue, p.16
,
, , p.19
, 21 1.4.1 Linear independence of LR B-Splines in 2D
, 25 2.3.2 Critical time increment comparison: Square Taylor bar impact 60 2.3.2.1 Model denition and boundary conditions
, 66 2.4.1 Isogeometric external surface tting
,
, Stable time step estimates for NURBS-based explicit dynamics, Computer Methods in Applied Mechanics and Engineering, vol.295, p.581605, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01215790
, Selective and reduced numerical integrations for NURBS-based isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, vol.284, p.732761, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01214741
, Développement d'éléments nis isogéométriques NURBS dans le code de calcul Abaqus, 2012.
, Génération de modèles NURBS volumiques issus de la CAO pour l'Analyse Isogéométrique, 12e Colloque national en calcul des structures, 2015.
, Isogeometric analysissuitable trivariate NURBS models from standard B-Rep models, Computer Methods in Applied Mechanics and Engineering, vol.307, p.256274, 2016.
, Towards an automatic isogeometric analysis suitable trivariate models generation-Application to geometric parametric analysis, Computer Methods in Applied Mechanics and Engineering, vol.316, p.623645, 2017.
, Weak Dirichlet boundary conditions for wall-bounded turbulent ows, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.49, p.48534862, 2007.
, Isogeometric analysis using T-splines, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.5, p.229263, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01517950
, The mortar nite element method for contact problems, Mathematical and Computer Modelling, vol.28, issue.4, p.263272, 1998.
, Nonlinear nite elements for continua and structures, INSA Lyon, tous droits réservés, vol.10, 2013.
, Stable time step estimation for multi-material Eulerian hydrocodes, Computer methods in applied mechanics and engineering, vol.167, issue.1-2, p.191205, 1998.
, A single surface contact algorithm for the postbuckling analysis of shell structures, Computer Methods in Applied Mechanics and Engineering, vol.78, issue.2, p.141163, 1990.
, A generalized nite element formulation for arbitrary basis functions: from isogeometric analysis to XFEM, International Journal for Numerical Methods in Engineering, vol.83, issue.6, p.765785, 2010.
, Isogeometric shell analysis: the Reissner-Mindlin shell, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.5, p.276289, 2010.
, A large deformation, rotation-free, isogeometric shell, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.13, p.13671378, 2011.
, Blended isogeometric shells, Computer Methods in Applied Mechanics and Engineering, vol.255, p.133146, 2013.
, Isogeometric Analysis in LS-DYNA: Using CAD-Geometry for Numerical Simulation, 10th European LS-DYNA Conference, 2015.
, Isogeometric nite element data structures based on Bézier extraction of NURBS, International Journal for Numerical Methods in Engineering, vol.87, issue.1-5, p.1547, 2011.
, Locking free isogeometric formulations of curved thick beams, Computer Methods in Applied Mechanics and Engineering, vol.245, p.144162, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00938536
, Ecient isogeometric NURBSbased solid-shell elements: Mixed formulation and B-method, Computer Methods in Applied Mechanics and Engineering, vol.267, p.86110, 2013.
, On the development of nurbs-based isogeometric solid shell elements: 2d problems and preliminary extension to 3d, Computational Mechanics, vol.52, issue.5, p.10851112, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00938246
, Development of a mixed displacement-stress formulation for the analysis of elastoplastic structures under small strains: Application to a locking-free, nurbs-based solid-shell element, Computer Methods in Applied Mechanics and Engineering, vol.295, p.543561, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01978240
, Some properties of LR-splines, Computer Aided Geometric Design, vol.30, issue.8, p.778794, 2013.
, A hierarchical construction of LR meshes in 2D, Computer Aided Geometric Design, vol.37, p.924, 2015.
, Selective mass scaling and critical time-step estimate for explicit dynamics analyses with solid-shell elements
DOI : 10.1016/j.compstruc.2012.10.021
, Computers & Structures, vol.127, p.3952, 2013.
, PetIGA: High-performance isogeometric analysis, 2013.
, Studies of renement and continuity in isogeometric structural analysis, Computer methods in applied mechanics and engineering, vol.196, p.41604183, 2007.
, Isogeometric Analysis: Toward Integration of CAD and FEA, vol.0470748737, p.9780470748732, 2009.
, GeoPDEs: a research tool for Isogeometric Analysis of PDEs, Advances in Engineering Software, vol.42, issue.12, p.10201034, 2011.
, A large deformation frictional contact formulation using NURBS-based isogeometric analysis, International Journal for Numerical Methods in Engineering, vol.87, issue.13, p.12781300, 2011.
, A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented Lagrangian method, Computational Mechanics, vol.49, issue.1, p.120, 2012.
, Isogeometric contact: a review, vol.37, p.85123, 2014.
, Computational methods for plasticity: theory and applications, INSA Lyon, tous droits réservés Bibliography, vol.33, 2011.
, Polynomial splines over hierarchical T-meshes, Graphical models, vol.70, issue.4, p.7686, 2008.
DOI : 10.1016/j.gmod.2008.03.001
, Isogeometric large deformation frictionless contact using T-splines, Computer methods in applied mechanics and engineering, vol.269, p.394414, 2014.
DOI : 10.1016/j.cma.2013.11.002
, Locally rened splines, 2010.
, Polynomial splines over locally rened box-partitions, Computer Aided Geometric Design, vol.30, issue.3, p.331356, 2013.
DOI : 10.1016/j.cagd.2012.12.005
, abqNURBS: implémentation d'éléments isogéométriques dans Abaqus et outils de pré-et post-traitement dédiés, 12e Colloque national en calcul des structures, 2015.
, Méthodes numériques innovantes pour les simulations robustes en mécanique des solides, 2014.
, Isogeometric analysis of nearly incompressible large strain plasticity, Computer Methods in Applied Mechanics and Engineering, vol.268, p.388416, 2014.
DOI : 10.1016/j.cma.2013.09.024
URL : https://hal.archives-ouvertes.fr/hal-00938598
, Hierarchical T-splines: Analysissuitability, Bézier extraction, and application as an adaptive basis for isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, vol.284, p.120, 2015.
, Dynamic implosion of underwater cylindrical shells: experiments and computations, International Journal of Solids and Structures, vol.50, issue.19, p.29432961, 2013.
DOI : 10.1016/j.ijsolstr.2013.05.006
URL : https://doi.org/10.1016/j.ijsolstr.2013.05.006
, Eigenvalues and stable time steps for the uniform strain hexahedron and quadrilateral, Journal of applied mechanics, vol.51, issue.1, p.3540, 1984.
, Bases and dimensions of bivariate hierarchical tensor-product splines, Journal of Computational and Applied Mathematics, vol.239, p.162178, 2013.
, THB-splines: The truncated basis for hierarchical splines, Computer Aided Geometric Design, vol.29, issue.7, p.485498, 2012.
, THB-splines: An eective mathematical technology for adaptive renement in geometric design and isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, vol.299, p.337365, 2016.
, Convergence of an ecient local least-squares tting method for bases with compact support, Computer Methods in Applied Mechanics and Engineering, vol.213, p.8492, 2012.
, LS-DYNA theory manual, Livermore software Technology corporation, vol.3, p.2531, 2006.
, Mass scaling and stable time step estimates for isogeometric analysis, International Journal for Numerical Methods in Engineering, vol.102, issue.3-4, p.671687, 2015.
, Optimal and reduced quadrature rules for tensor product and hierarchically rened splines in isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, vol.316, p.9661004, 2017.
, The mathematical theory of plasticity, vol.11, 1998.
, Analyse isogéométrique pour les probleèmes d'optimisation de forme des structures coques, 2017.
, The Computer Journal, vol.5, issue.1, p.1016, 1962.
, The nite element method: linear static and dynamic nite element analysis, Courier, 2012.
, Isogeometric analysis: CAD, nite elements, NURBS, exact geometry and mesh renement, Computer Methods in Applied Mechanics and Engineering, vol.194, p.41354195, 2005.
, Ecient quadrature for NURBS-based isogeometric analysis. Computer methods in applied mechanics and engineering, vol.199, p.301313, 2010.
, Isogeometric analysis using LR B-splines, Computer Methods in Applied Mechanics and Engineering, vol.269, p.471514, 2014.
, On the similarities and dierences between Classical Hierarchical, Truncated Hierarchical and LR Bsplines, Computer Methods in Applied Mechanics and Engineering, vol.291, pp.64-101, 2015.
, Numerical and Experimental Study of Single-Walled and Double-Walled Columns under Dynamic Axial Crushing, Journal of Mechanical Engineering, vol.9, issue.2, p.5372, 2012.
, Geometry+ simulation modules: Implementing isogeometric analysis, vol.14, pp.961-962, 2014.
, Mixed Galerkin and least-squares formulations for isogeometric analysis, 2014.
, New B-spline nite element approach for geometrical design and mechanical analysis, International Journal for Numerical Methods in Engineering, vol.41, issue.3, p.435458, 1998.
, A simple benchmark for impact, p.3135, 1990.
, Modied T-splines, Computer Aided Geometric Design, vol.30, issue.9, p.827843, 2013.
, Isogeometric contact analysis using mortar method, International Journal for Numerical Methods in Engineering, vol.89, issue.12, pp.1559-1581, 2012.
, Algorithms and data structures for truncated hierarchical B-splines, International Conference on Mathematical Methods for Curves and Surfaces, p.304323, 2012.
, Rhino 3D to Abaqus: A T-Spline Based Isogeometric Analysis Software Framework, Advances in Computational Fluid-Structure Interaction and Flow Simulation, pp.271-281, 2016.
, Integrating CAD with Abaqus: a practical isogeometric analysis software platform for industrial applications, Computers & Mathematics with Applications, vol.74, issue.7, p.16481660, 2017.
, Volumetric T-spline construction using Boolean operations, Engineering with Computers, vol.30, issue.4, p.425439, 2014.
, Handling extraordinary nodes with weighted T-spline basis functions, Procedia Engineering, vol.124, p.161173, 2015.
, Weighted T-splines with application in reparameterizing trimmed NURBS surfaces, Computer Methods in Applied Mechanics and Engineering, vol.295, p.108126, 2015.
, IGA-ADS: isogeometric analysis FEM using ADS solver, Computer Physics Communications, vol.217, p.99116, 2017.
, Isogeometric contact analysis: Geometric basis and formulation for frictionless contact, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.5-8, p.726741, 2011.
, A weighted point-based formulation for isogeometric contact, Computer Methods in Applied Mechanics and Engineering, vol.308, p.7395, 2016.
, A point to segment contact formulation for isogeometric, NURBS based nite elements, Computer Methods in Applied Mechanics and Engineering, vol.255, p.2739, 2013.
, On the numerical integration of trimmed isogeometric elements, Computer Methods in Applied Mechanics and Engineering, vol.284, p.165185, 2015.
, Master's thesis, Norges teknisk-naturvitenskapelige universitet, Fakultet for ingeniørvitenskap og teknologi, Institutt for konstruksjonsteknikk, 2011.
, Extended isogeometric analysis for strong and weak discontinuities, Isogeometric methods for numerical simulation, p.21120, 2015.
, Isogeometric analysis: an overview and computer implementation aspects, Mathematics and Computers in Simulation, vol.117, p.89116, 2015.
, Rotation free isogeometric thin shell analysis using PHT-splines, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.47, p.34103424, 2011.
, Selective mass scaling for thin walled structures modeled with tri-linear solid elements, INSA Lyon, tous droits réservés Bibliography [81] L Olovsson, M Unosson, and K Simonsson, vol.34, p.134136, 2004.
, Selective mass scaling for explicit nite element analyses, International Journal for Numerical Methods in Engineering, vol.63, issue.10, p.14361445, 2005.
, Computationally ecient explicit nonlinear analyses using reduced integration-based solid-shell nite elements, Computer Methods in Applied Mechanics and Engineering, vol.268, p.141159, 2014.
, Practical aspects of numerical time integration, Computers & Structures, vol.7, issue.3, p.343353, 1977.
, Igatools: An isogeometric analysis library, SIAM Journal on Scientic Computing, vol.37, issue.4
, The NURBS Book, 1997.
DOI : 10.1007/978-3-642-97385-7
, An experimental study on the deformation and fracture modes of steel projectiles during impact
, Materials & Design, vol.51, p.242256, 2013.
, A numerical study on the deformation and fracture modes of steel projectiles during Taylor bar impact tests, International Journal of Solids and Structures, vol.51, issue.3-4, p.808821, 2014.
, PJ Roache. Computational Fluid Dynamics, 1976.
, Google Scholar, 1980.
, From the nite element analysis to the isogeometric analysis in an object oriented computing environment, Advances in Engineering Software, vol.44, p.116125, 2012.
, An isogeometric design-through-analysis methodology based on adaptive hierarchical renement of NURBS, immersed boundary methods, and Tspline CAD surfaces, Computer Methods in Applied Mechanics and Engineering, vol.249, p.116150, 2012.
, Isogeometric collocation: Cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations, Computer Methods in Applied Mechanics and Engineering, vol.267, p.170232, 2013.
DOI : 10.1002/pamm.201310049
URL : https://onlinelibrary.wiley.com/doi/pdf/10.1002/pamm.201310049
, Reduced Bézier element quadrature rules for quadratic and cubic splines in isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, vol.277, p.145, 2014.
DOI : 10.1016/j.cma.2014.04.008
, Local renement of analysis-suitable T-splines, Computer Methods in Applied Mechanics and Engineering, vol.213, p.206222, 2012.
DOI : 10.21236/ada555339
URL : http://www.dtic.mil/dtic/tr/fulltext/u2/a555339.pdf
,
, In ACM transactions on graphics, vol.22, p.477484, 2003.
,
, T-spline simplication and local renement, In ACM transactions on graphics, vol.23, p.276283, 2004.
, Hierarchical NURBS in frictionless contact, Computer Methods in Applied Mechanics and Engineering, vol.299, p.161186, 2016.
DOI : 10.1016/j.cma.2015.11.006
URL : http://repository.bilkent.edu.tr/bitstream/11693/36862/1/Hierarchical_NURBS_in_Frictionless_Contact.pdf
, Contact treatment in isogeometric analysis with NURBS, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.9, p.11001112, 2011.
DOI : 10.1016/j.cma.2010.11.020
, Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS, Computer Methods in Applied Mechanics and Engineering, vol.209, p.115128, 2012.
DOI : 10.1016/j.cma.2011.10.014
URL : http://repository.bilkent.edu.tr/bitstream/11693/21612/1/Three-dimensional%20mortar-based%20frictional%20contact%20treatment%20in%20isogeometric%20analysis%20with%20NURBS.pdf
, Elasticity theory. M: Science, 1975.
, A hierarchical approach to adaptive local renement in isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.49, p.35543567, 2011.
, Adaptive isogeometric analysis using rational PHT-splines, Computer-Aided Design, vol.43, issue.11, p.14381448, 2011.
, An optimization approach for constructing trivariate B-spline solids, Computer-Aided Design, vol.46, p.179191, 2014.
, Truncated T-splines: Fundamentals and methods, Computer Methods in Applied Mechanics and Engineering, vol.316, p.349372, 2017.
, The algebraic eigenvalue problem, Handbook for Automatic Computation, vol.II, 1971.
, Radioss theoretical manual. MECALOG archives, 1999.
, Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization, Computer Methods in Applied Mechanics and Engineering, vol.328, p.175200, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01599319
, A segmentation-free isogeometric extended mortar contact method, 2017.
, Une approche isogéométrique pour la thermomécanique en grandes transformations dans un contexte multiphysique à objets, 2015.