A point to segment contact formulation for isogeometric, NURBS based finite elements

Hughes, 1977, A finite element method for large displacement contact and impact problems, 468

J.O. Hallquist, Nike2D: an implicit, finite deformation, finite element code for analyzing the static and dynamic response of two-dimensional solids, Tech. Rep. UCRL-52678, Lawrence Livermore National Laboratory, University of California, Livermore, 1979.

Bathe, 1985, A solution method for planar and axisymmetric contact problems, Int. J. Numer. Methods Engrg., 21, 65, 10.1002/nme.1620210107

Hallquist, 1985, Sliding interfaces with contact-impact in large-scale lagrange computations, Comput. Methods Appl. Mech. Engrg., 51, 107, 10.1016/0045-7825(85)90030-1

Wriggers, 1985, A note on tangent stiffness for fully nonlinear contact problems, Commun. Appl. Numer. Methods, 1, 199, 10.1002/cnm.1630010503

Wriggers, 1990, Finite element formulation of large deformation impact-contact problems with friction, Comput. Struct., 37, 319, 10.1016/0045-7949(90)90324-U

Laursen, 1993, A continuum-based finite element formulation for the implicit solution of multibody, large deformation-frictional contact problems, Int. J. Numer. Methods Engrg., 36, 3451, 10.1002/nme.1620362005

Simo, 1985, A perturbed lagrangian formulation for the finite element solution of contact problems, Comput. Methods Appl. Mech. Engrg., 50, 163, 10.1016/0045-7825(85)90088-X

Papadopoulos, 1992, A mixed formulation for the finite element solution of contact problems, Computer Methods in Applied Mechanics and Engineering, 94, 373, 10.1016/0045-7825(92)90061-N

Papadopoulos, 1993, A simple algorithm for three-dimensional finite element analysis of contact problems, Comput. Struct., 46, 1107, 10.1016/0045-7949(93)90096-V

Zavarise, 1998, A segment-to-segment contact strategy, Math. Comput. Model., 28, 497, 10.1016/S0895-7177(98)00138-1

El-Abbasi, 2001, Stability and patch test performance of contact discretizations and a new solution algorithm, Comput. Struct., 79, 1473, 10.1016/S0045-7949(01)00048-7

C. Bernardi, Y. Maday, A. Patera, Domain decomposition by the mortar element method, in: H. Kasper, M. Garby (Eds.), Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters: Proceedings of the NATO Advanced Research Workshop on Asymptotic-Induced Numerical Methods for Partial Differential Equations, Critical Parameters, and Domain Decomposition, Science Series C, vol. 384, 25–28 May 1993, Beaune, Frankreich, NATO, 1993, pp. 269–286.

C. Bernardi, Y. Maday, A. Patera, A new nonconforming approach to domain decomposition: the mortar element method, in: H. Brezis, J. Lions (Eds.), Nonlinear Partial Differential Equations and Their Applications, Collége de France Seminar, vol. 12, 1994, pp. 13–51.

Ben Belgacem, 1998, The mortar finite element method for contact problems, Math. Comput. Model., 28, 263, 10.1016/S0895-7177(98)00121-6

Ben Belgacem, 2000, Numerical simulation of some variational inequalities arisen from unilateral contact problems by the finite element methods, SIAM J. Numer. Anal., 37, 1198, 10.1137/S0036142998347966

Wohlmuth, 2003, Monotone multigrid methods on nonmatching grids for nonlinear multibody contact problems, SIAM J. Sci. Comput., 25, 324, 10.1137/S1064827502405318

McDewitt, 2000, A mortar-finite element formulation for frictional contact problems, Int. J. Numer. Methods Engrg., 48, 1525, 10.1002/1097-0207(20000810)48:10<1525::AID-NME953>3.0.CO;2-Y

Yang, 2005, Two dimensional mortar contact methods for large deformation frictional sliding, Int. J. Numer. Methods Engrg., 62, 1183, 10.1002/nme.1222

Puso, 2004, A mortar segment-to-segment contact method for large deformation solid mechanics, Comput. Methods Appl. Mech. Engrg., 193, 601, 10.1016/j.cma.2003.10.010

Fischer, 2005, Frictionless 2D contact formulation for finite deformations based on the mortar method, Comput. Mech., 36, 226, 10.1007/s00466-005-0660-y

Wohlmuth, 2000, A mortar finite element method using dual spaces for the lagrange multiplier, SIAM J. Numer. Anal., 38, 989, 10.1137/S0036142999350929

Wohlmuth, 2001, Discretization Methods and Iterative Solvers Based on Domain Decomposition, vol. 17

Hüeber, 2005, A primal-dual active set strategy for non-linear multibody contact problems, Comput. Methods Appl. Mech. Engrg., 194, 3147, 10.1016/j.cma.2004.08.006

Hartmann, 2007, Unilateral non-linear dynamic contact of thin-walled structures using a primal-dual active set strategy, Int. J. Numer. Methods Engrg., 70, 883, 10.1002/nme.1894

Hartmann, 2008, A mortar based contact formulation for non-linear dynamics using dual lagrange multipliers, Finite Elem. Anal. Des., 44, 245, 10.1016/j.finel.2007.11.018

Popp, 2009, A finite deformation mortar contact formulation using a primal-dual active set strategy, Int. J. Numer. Methods Engrg., 79, 1354, 10.1002/nme.2614

Cichosz, 2011, Consistent treatment of boundaries with mortar contact formulations using dual lagrange multipliers, Comput. Methods Appl. Mech. Engrg., 200, 1317, 10.1016/j.cma.2010.11.004

Padmanabhan, 2001, A framework for development of surface smoothing procedures in large deformation frictional contact analysis, Finite Elem. Anal. Des., 37, 173, 10.1016/S0168-874X(00)00029-9

Wriggers, 2001, Smooth c1-interpolations for two-dimensional frictional contact problems, Int. J. Numer. Methods Engrg., 51, 1469, 10.1002/nme.227

Puso, 2002, A 3d contact smoothing method using Gregory patches, Int. J. Numer. Methods Engrg., 54, 1161, 10.1002/nme.466

Konyukhov, 2009, Incorporation of contact for high-order finite elements in covariant form, Comput. Methods Appl. Mech. Engrg., 198, 1213, 10.1016/j.cma.2008.04.023

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

Temizer, 2011, Contact treatment in isogeometric analysis with NURBS, Comput. Methods Appl. Mech. Engrg., 200, 1100, 10.1016/j.cma.2010.11.020

Lu, 2011, Isogeometric contact analysis: geometric basis and formulation for frictionless contact, Comput. Methods Appl. Mech. Engrg., 200, 726, 10.1016/j.cma.2010.10.001

M. Matzen, 2D NURBS Kollokations-Kontaktformulierung, Master’s Thesis, Arbeit Nr. 10/03, Institut für Baustatik, Universität Stuttgart, 2010.

Zavarise, 2009, A modified node-to-segment algorithm passing the contact patch test, Int. J. Numer. Methods Engrg., 79, 379, 10.1002/nme.2559

Zavarise, 2009, The node-to-segment algorithm for 2d frictionless contact: classical formulation and special cases, Comput. Methods Appl. Mech. Engrg., 198, 3428, 10.1016/j.cma.2009.06.022

Kikuchi, 1988

Konyukhov, 2008, On the solvability of closest point projection procedures in contact analysis: analysis and solution strategy for surfaces of arbitrary geometry, Comput. Methods Appl. Mech. Engrg., 197, 3045, 10.1016/j.cma.2008.02.009

Konyukhov, 2004

de Boor, 1972, On calculation with b-splines, J. Approx. Theory, 6, 50, 10.1016/0021-9045(72)90080-9

De Lorenzis, 2011, A large deformation frictional contact formulation using NURBS-based isogeometric analysis, Int. J. Numer. Methods Engrg., 87, 1278, 10.1002/nme.3159

Wriggers, 2002

Auricchio, 2010, Isogeometic collocation methods, Math. Models Methods Appl. Sci., 20, 2075, 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

Beiraõ da Veiga, 2012, Avoiding shear locking for the Timoshenko beam problem via isogeometric collocation methods, Comput. Methods Appl. Mech. Engrg., 38, 10.1016/j.cma.2012.05.020

Demko, 1985, On the existence of interpolating projections onto spline spaces, J. Approx. Theory, 43, 151, 10.1016/0021-9045(85)90123-6

Jator, 2007, A high order b-spline collocation method for linear boundary value problems, Appl. Math. Comput., 191, 100, 10.1016/j.amc.2007.02.027

Botella, 2002, On a collocation method for the solution of Navier–Stokes equations, Comput. Fluids, 31, 397, 10.1016/S0045-7930(01)00058-5

Boor, 1994

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

Bazilevs, 2010, Isogeometric analysis using t-splines, Comput. Methods Appl. Mech. Engrg., 199, 229, 10.1016/j.cma.2009.02.036

Höllig, 1987

Vuong, 2011, A hierarchical approach to adaptive local refinement in isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 200, 3554, 10.1016/j.cma.2011.09.004

D. Schillinger, L. Ded, M.A. Scott, J.A. Evans, M.J. Borden, E. Rank, T.J. Hughes, An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and t-spline CAD surfaces, Comput. Methods Appl. Mech. Engrg. (2012), submitted for publication.

Kleiss, 2012, Enhancing isogeometric analysis by a finite element-based local refinement strategy, Comput. Methods Appl. Mech. Engrg., 213–216, 168, 10.1016/j.cma.2011.11.013