- -

A modified perturbed Lagrangian formulation for contact problems

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

A modified perturbed Lagrangian formulation for contact problems

Mostrar el registro sencillo del ítem

Ficheros en el ítem

Thumbnail
Nombre: StabilizedContact ...
Tamaño: 2.071Mb
Formato: PDF
Descripción: Versión del Autor.
Abrir
[Cerrado]
Nombre: Tur;Albelda;J.M. ...
Tamaño: 2.684Mb
Formato: PDF
Descripción: Versión editorial
Solicitar una copia al autor
dc.contributor.author Tur Valiente, Manuel es_ES
dc.contributor.author Albelda Vitoria, José es_ES
dc.contributor.author Navarro Jiménez, José Manuel es_ES
dc.contributor.author Ródenas García, Juan José es_ES
dc.date.accessioned 2016-07-08T18:02:44Z
dc.date.available 2016-07-08T18:02:44Z
dc.date.issued 2015-04
dc.identifier.issn 0178-7675
dc.identifier.uri http://hdl.handle.net/10251/67385
dc.description.abstract The aim of this work is to propose a formulation to solve both small and large deformation contact problems using the finite element method. We consider both standard finite elements and the so-called immersed boundary elements. The method is derived from a stabilized Nitsche formulation. After introduction of a suitable Lagrange multiplier discretization the method can be simplified to obtain a modified perturbed Lagrangian formulation. The stabilizing term is iteratively computed using a smooth stress field. The method is simple to implement and the numerical results show that it is robust. The optimal convergence rate of the finite element solution can be achieved for linear elements. es_ES
dc.description.sponsorship The authors wish to thank the Spanish Ministerio de Economia y Competitividad for the financial support received through the DPI Project DPI2013-46317-R. en_EN
dc.language Inglés es_ES
dc.publisher Springer Verlag (Germany) es_ES
dc.relation.ispartof Computational Mechanics es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Contact es_ES
dc.subject Stabilized es_ES
dc.subject Penalty es_ES
dc.subject Large deformation es_ES
dc.subject Perturbed Lagrangian es_ES
dc.subject.classification INGENIERIA MECANICA es_ES
dc.title A modified perturbed Lagrangian formulation for contact problems es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s00466-015-1133-6
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//DPI2013-46317-R/ES/PERSONALIZACION DE IMPLANTES MEDIANTE MODELOS DE ELEMENTOS FINITOS A PARTIR DE IMAGENES MEDICAS 3D/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Ingeniería Mecánica y de Materiales - Departament d'Enginyeria Mecànica i de Materials es_ES
dc.description.bibliographicCitation Tur Valiente, M.; Albelda Vitoria, J.; Navarro Jiménez, JM.; Ródenas García, JJ. (2015). A modified perturbed Lagrangian formulation for contact problems. Computational Mechanics. 55(4):737-754. https://doi.org/10.1007/s00466-015-1133-6 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1007/s00466-015-1133-6 es_ES
dc.description.upvformatpinicio 737 es_ES
dc.description.upvformatpfin 754 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 55 es_ES
dc.description.issue 4 es_ES
dc.relation.senia 282458 es_ES
dc.identifier.eissn 1432-0924
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
dc.description.references Annavarapu C, Hautefeuille M, Dolbow J (2012) A robust Nitsche’s formulation for interface problems. Comput Methods Appl Mech Eng 228:44–54 es_ES
dc.description.references Annavarapu C, Hautefeuille M, Dolbow J (2012) Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods. Int J Numer Methods Eng 92(2):206–228 es_ES
dc.description.references Annavarapu C, Hautefeuille M, Dolbow J (2013) A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. Part II: intersecting interfaces. Comput Methods Appl Mech Eng 267:318–341 es_ES
dc.description.references Annavarapu C, Hautefeuille M, Dolbow J (2014) A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. Part I: single interface. Comput Methods Appl Mech Eng 268:417–436 es_ES
dc.description.references Baiges J, Codina R, Henke F, Shahmiri S, Wall WA (2012) A symmetric method for weakly imposing Dirichlet boundary conditions in embedded finite element meshes. Int J Numer Methods Eng 90(5):636–658 es_ES
dc.description.references Barbosa HJC, Hughes TJR (1992) Circumventing the Babuska–Brezzi condition in mixed finite element approximations of elliptic variational inequalities. Comput Methods Appl Mech Eng 97(2):193–210 es_ES
dc.description.references Bechet E, Moes N, Wohlmuth B (2009) A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method. Int J Numer Methods Eng 78(8):931–954 es_ES
dc.description.references Belgacem F, Hild P, Laborde P (1998) The mortar finite element method for contact problems. Math Comput Model 28(4–8):263–271 es_ES
dc.description.references Brezzi F (1974) On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. ESAIM 8(R2):129–151 es_ES
dc.description.references Brezzi F, Fortin M (1991) Mixed and hybrid finite element methods. Springer, New York es_ES
dc.description.references Burman E, Hansbo P (2010) Fictitious domain finite element methods using cut elements: I. A stabilized Lagrange multiplier method. Comput Methods Appl Mech Eng 199:2680–2686 es_ES
dc.description.references Burman E, Hansbo P (2012) Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method. Appl Numer Math 62(4):328–341 es_ES
dc.description.references Chouly F, Hild P, Renard Y (2013) Symmetric and non-symmetric variants of Nitsche’s method for contact problems in elasticity: theory and numerical experiments. doi: 10.1007/s00466-012-0780-0 es_ES
dc.description.references Codina R, Baiges J (2009) Approximate imposition of boundary conditions in immersed boundary methods. Int J Numer Methods Eng 80(11):1379–1405 es_ES
dc.description.references Coorevits P, Hild P, Lhalouani K, Sassi T (2001) Mixed finite element methods for unilateral problems: convergence analysis and numerical studies. Math Comput 71(237):1–25 es_ES
dc.description.references ElAbbasi N, Bathe KJ (2001) Stability and patch test performance of contact discretizations and a new solution algorithm. Comput Struct 79:1473–1486 es_ES
dc.description.references Fischer K, Wriggers P (2005) Frictionless 2D contact formulations for finite deformations based on the mortar method. Comput Mech 36:226–244 es_ES
dc.description.references Fischer K, Wriggers P (2005) Mortar based frictional contact formulation for higher order interpolations using the moving friction cone. Comput Methods Appl Mech Eng 195:5020–5036 es_ES
dc.description.references Gerstenberger A, Wall WA (2010) An embedded Dirichlet formulation for 3D continua. Int J Numer Methods Eng 82(5):537–563 es_ES
dc.description.references Gitterle M, Popp A, Gee MW, Wall WA (2010) A dual mortar approach for 3D finite deformation contact with consistent linearization. Int J Numer Methods Eng 84(5):543–571 es_ES
dc.description.references Gravouil A, Pierres E, Baietto M (2011) Stabilized global-local X-FEM for 3D non-planar frictional contact using relevant meshes. Int J Numer Methods Eng 88(13):1449–1475 es_ES
dc.description.references Hammer ME (2013) Frictional mortar contact for finite deformation problems with synthetic contact kinematics. Comput Mech 51(6):975–998 es_ES
dc.description.references Hansbo P, Lovadina C, Perugia I, Sangalli G (2005) A Lagrange multiplier method for the finite element solution of elliptic interface problems using non-matching meshes. Numer Math 100:91– 115 es_ES
dc.description.references Hartmann S, Ramm E (2008) A mortar based contact formulation for non-linear dynamics using dual Lagrange multipliers. Finite Elem Anal Des 44:245–258 es_ES
dc.description.references Haslinger J, Renard Y (2009) A new fictitious domain approach inspired by the extended finite element method. SIAM J Numer Anal 47(2):1474–1499. doi: 10.1137/070704435 es_ES
dc.description.references Heintz P, Hansbo P (2006) Stabilized Lagrange multiplier methods for bilateral contact with friction. Comput Methods Appl Mech Eng 195:4323–4333 es_ES
dc.description.references Hild P (2000) Numerical implementation of two nonconforming finite element methods for unilateral contact. Comput Methods Appl Mech Eng 184:99–123 es_ES
dc.description.references Hild P, Laborde P (2002) Quadratic finite element methods for unilaterial contact problems. Appl Numer Math 41:401–421 es_ES
dc.description.references Hild P, Renard Y (2010) A stabilized Lagrange multiplier method for the finite element approximation of contact problems in elastostatics. Numer Math 115(101–129):2456–2471 es_ES
dc.description.references Hueber S, Mair M, Wohlmuth B (2005) A priori error estimates and an inexact primal-dual active set strategy for linear and quadratic finite elements applied to multibody contact problems. Appl Numer Math 54:555–576 es_ES
dc.description.references Hueber S, Stadler G, Wohlmuth BI (2008) A primal-dual active set algorithm for three-dimensional contact problems with coulomb friction. SIAM J Sci Comput 30(2):572–596 es_ES
dc.description.references Hueber S, Wohlmuth B (2005) A primal-dual active set strategy for non-linear multibody contact problems. Comput Methods Appl Mech Eng 194:3147–3166 es_ES
dc.description.references Laursen T (2002) Computational contact and impact mechanics. Springer, Berlin es_ES
dc.description.references Liu F, Borja RI (2010) Stabilized low-order finite elements for frictional contact with the extended finite element method. Comput Methods Appl Mech Eng 199(37–40):2456–2471 es_ES
dc.description.references McDevitt T, Laursen T (2000) A mortar-finite element formulation for frictional contact problems. Int J Numer Methods Eng 48:1525–1547 es_ES
dc.description.references Nadal E, Ródenas JJ, Albelda J, Tur M, Tarancón JE, Fuenmayor FJ (2013) Efficient finite element methodology based on cartesian grids: application to structural shape optimization. Abstr Appl Anal, pp 1–19 es_ES
dc.description.references Nistor I, Guiton M, Massin P, Moes N, Geniaut S (2009) An X-FEM approach for large sliding contact along discontinuities. Int J Numer Meth Eng 78(12):1407–1435 es_ES
dc.description.references Popp A, Gitterle M, Gee MW, Wall WA (2010) Finite deformation frictional mortar contact using a semi-smooth Newton method with consistent linearization. Int J Numer Methods Eng 83(11):1428–1465 es_ES
dc.description.references Puso M (2004) A 3D mortar method for solid mechanics. Int J Numer Methods Eng 59:315–336 es_ES
dc.description.references Puso M, Laursen T (2004) A mortar segment-to-segment contact method for large deformation solid mechanics. Comput Methods Appl Mech Eng 193:601–629 es_ES
dc.description.references Puso M, Laursen T (2004) A mortar segment-to-segment frictional contact method for large deformations. Comput Methods Appl Mech Eng 193:4891–4913 es_ES
dc.description.references Puso M, Laursen T, Solberg J (2008) A segment-to-segment mortar contact method for quadratic elements and large deformations. Comput Methods Appl Mech Eng 197:555–566 es_ES
dc.description.references Ródenas J, Tur M, Fuenmayor F, Vercher A (2007) Improvement of the superconvergent patch recovery technique by the use of constraint equations: the SPR-C technique. Int J Numer Methods Eng 70:705–727 es_ES
dc.description.references Saad Y (2003) Iterative methods for sparse linear systems., Applied Mathematical SciencesSociety for Industrial and Applied Mathematics, Philadelphia es_ES
dc.description.references Sanders JD, Laursen TA, Puso M (2012) A Nitsche embedded mesh method. Comput Mech 49:243–257 es_ES
dc.description.references Schott B, Wall W (2014) A new face-oriented stabilized XFEM approach foir 2D and 3D incompressible Navier–Stokes equations. Comput Methods Appl Mech Eng 276:233–265 es_ES
dc.description.references Simo J, Wriggers P, Taylor R (1985) A perturbed Lagrangian formulation for the finite element solution of contact problems. Comput Methods Appl Mech Eng 50:163–180 es_ES
dc.description.references Stenberg R (1995) On some techniques for approximating boundary conditions in the finite element method. J Comput Appl Math 63:139–148 es_ES
dc.description.references Strouboulis T, Copps K, Babuška I (2000) The generalized finite element method: an example of its implementation and illustration of its performance. Int J Numer Methods Eng 47:1401–1417 es_ES
dc.description.references Tur M, Fuenmayor F, Wriggers P (2009) A mortar-based frictional contact formulation for large deformations using Lagrange multipliers. Comput Methods Appl Mech Eng 198:2860–2873 es_ES
dc.description.references Tur M, Albelda J, Nadal E, Ródenas JJ (2014) Imposing Dirichlet boundary conditions in hierarchical Cartesian meshes by means of stabilized Lagrange multipliers. Int J Numer Methods Eng 98(6):399–417 es_ES
dc.description.references Tur M, Albelda J, Marco O, Ródenas JJ (2014) Stabilized method to impose Dirichlet boundary conditions using a smooth stress field. Comput Methods Appl M, Under review es_ES
dc.description.references Wohlmuth B, Popp A, Gee MW, Wall WA (2012) An abstract framework for a priori estimates for contact problems in 3d with quadratic finite elements. Comput Mech 49:735–747 es_ES
dc.description.references Wriggers P (2002) Computational contact mechanics. Wiley, Chichester es_ES
dc.description.references Yang B, Laursen T, Meng X (2005) Two dimensional mortar contact methods for large deformation frictional sliding. Int J Numer Methods Eng 62:1183–1225 es_ES
dc.description.references Zavarise G, Wriggers P (1998) A segment-to-segment contact strategy. Mathe Comput Model 28(4–8):497–515 es_ES
dc.description.references Zavarise G, Wriggers P (2008) A formulation for frictionless contact problems using a weak form introduced by Nitsche. Comput Mech 41:407–420 es_ES
dc.description.references Zavarise G, De Lorenzis L (2009) A modified node-to-segment algorithm passing the contact patch test. Int J Numer Methods Eng 79:379–416 es_ES
dc.description.references Zienkiewicz O, Zhu J (1992) Superconvergent patch recovery techniques and a posteriori error estimation., Part I: the recovery technique. Int J Numer Methods Eng 33:1331–1364 es_ES


Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem