Isogeometric collocation: Neumann boundary conditions and contact

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 Cottrell, 2009 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 Groß mann, 2012, Isogeometric simulation of turbine blades for aircraft engines, Comput. Aided Geom. Design, 29, 519, 10.1016/j.cagd.2012.03.002 Hughes, 2010, Efficient quadrature for NURBS-based isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 199, 301, 10.1016/j.cma.2008.12.004 Auricchio, 2012, A simple algorithm for obtaining nearly optimal quadrature rules for NURBS-based isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 249–252, 15, 10.1016/j.cma.2012.04.014 Auricchio, 2010, Isogeometric collocation methods, Mathematical Models and Methods in Applied Sciences, 20, 10.1142/S0218202510004878 Auricchio, 2012, Isogeometric collocation for elastostatics and explicit dynamics, Comput. Methods Appl. Mech. Engrg., 249–252, 2, 10.1016/j.cma.2012.03.026 Bischoff, 2004, Models and Finite Elements for Thin-walled Structures, 59 Schillinger, 2013, Isogeometric collocation: cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations, Comput. Methods Appl. Mech. Engrg., 267, 170, 10.1016/j.cma.2013.07.017 Beirão da Veiga, 2012, Avoiding shear locking for the Timoshenko beam problem via isogeometric collocation methods, Comput. Methods Appl. Mech. Engrg., 241–244, 38, 10.1016/j.cma.2012.05.020 Auricchio, 2013, Locking-free isogeometric collocation methods for spatial Timoshenko rods, Comput. Methods Appl. Mech. Engrg., 263, 113, 10.1016/j.cma.2013.03.009 Oñate, 1996, A finite point method in computational mechanics. Application to convective transport and fluid flow, Internat. J. Numer. Methods Engrg, 39, 3839, 10.1002/(SICI)1097-0207(19961130)39:22<3839::AID-NME27>3.0.CO;2-R Aluru, 2000, A point collocation method based on reproducing kernel approximation, Internat. J. Numer. Methods Engrg, 47, 1083, 10.1002/(SICI)1097-0207(20000228)47:6<1083::AID-NME816>3.0.CO;2-N Zhang, 2001, Least-squares collocation meshless method, Internat. J. Numer. Methods Engrg, 51, 1089, 10.1002/nme.200 Kim, 2003, Point collocation methods using the fast moving least-square reproducing kernel approximation, Internat. J. Numer. Methods Engrg, 56, 1445, 10.1002/nme.618 Hu, 2007, Weighted radial basis collocation method for boundary value problems, Internat. J. Numer. Methods Engrg, 69, 2736, 10.1002/nme.1877 Nguyen, 2008, Meshless methods: A review and computer implementation aspects, Math. Comput. Simul., 79, 763, 10.1016/j.matcom.2008.01.003 Hu, 2011, Error analysis of collocation method based on reproducing kernel approximation, Numer. Methods Partial Differential Equations, 27, 554, 10.1002/num.20539 Chi, 2013, A gradient reproducing kernel collocation method for boundary value problems, Internat. J. Numer. Methods Engrg, 93, 1381, 10.1002/nme.4432 Piegl, 1996 Grisvard, 2011 Grisvard, 1986, Problemes aux limites dans les polygones. Mode d’emploi, Bull. Dir, Etud. Rech., Ser C Laursen, 2002 Wriggers, 2006 Sauer, 2013, A computational contact formulation based on surface potentials, Comput. Methods Appl. Mech. Engrg., 253, 369, 10.1016/j.cma.2012.09.002 Zavarise, 2009, A modified node-to-segment algorithm passing the contact patch test, Internat. J. Numer. Methods Engrg, 79, 379, 10.1002/nme.2559 Fischer, 2005, Frictionless 2D contact formulations for finite deformations based on the mortar method, Comput. Mech., 36, 226, 10.1007/s00466-005-0660-y Temizer, 2011, Contact treatment in isogeometric analysis with NURBS, Comput. Methods Appl. Mech. Engrg., 200, 1100, 10.1016/j.cma.2010.11.020 De Lorenzis, 2011, A large deformation frictional contact formulation using NURBS-based isogeometric analysis, Internat. J. Numer. Methods Engrg, 87, 1278, 10.1002/nme.3159 Dimitri, 2014, Isogeometric large deformation frictionless contact using T-splines, Comput. Methods Appl. Mech. Engrg., 269, 394, 10.1016/j.cma.2013.11.002 Puso, 2004, A mortar segment-to-segment frictional contact method for large deformations, Comput. Methods Appl. Mech. Engrg., 193, 4891, 10.1016/j.cma.2004.06.001 Temizer, 2012, Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS, Comput. Methods Appl. Mech. Engrg., 209–212, 115, 10.1016/j.cma.2011.10.014 De Lorenzis, 2012, A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented Lagrangian method, Comput. Mech., 49, 1, 10.1007/s00466-011-0623-4 Papadopoulos, 1995, A novel finite element formulation for frictionless contact problems, Internat. J. Numer. Methods Engrg, 38, 2603, 10.1002/nme.1620381507 Taylor, 1991, On a patch test for contact problems in two dimensions, 690 Matzen, 2013, A point to segment contact formulation for isogeometric, NURBS based finite elements, Comput. Methods Appl. Mech. Engrg., 255, 27, 10.1016/j.cma.2012.11.011