Skip to main content
Erschienen in: Meccanica 6/2018

09.10.2017 | Novel Computational Approaches to Old and New Problems in Mechanics

Numerical solution of smooth and rough contact problems

verfasst von: Francesco Marmo, Ferdinando Toraldo, Alessandra Rosati, Luciano Rosati

Erschienen in: Meccanica | Ausgabe 6/2018

Einloggen

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

A general procedure for the numerical solution of three-dimensional normal and tangential contact problems for non-conforming bodies of arbitrary shape is presented. The proposed procedure is based on the interpolation of known analytical solutions relating surface displacements of an elastic half-space subjected to pyramidal distributions of normal and tangential surface tractions. These formulas are used to interpolate unknown pressure distributions on the contact zone of two elastic bodies in contact. The proposed interpolation significantly reduces the computational burden of the numerical procedure required to interpolate the actual pressure distribution and to determine the initially unknown contact region. It amounts to expressing the contact pressure as a function of the elastic parameters of the two bodies, the distance between their surfaces and the relative displacement between two far-points pertaining to the bodies in contact. The procedure has been validated by comparison with classical contact problems and the results show excellent agreement with existing analytical and numerical solutions.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Ahmadi N, Keer L, Mura T (1983) Non-Hertzian contact stress analysis for an elastic half-space normal and sliding contact. Int J Solids Struct 19(4):357–373CrossRefMATH Ahmadi N, Keer L, Mura T (1983) Non-Hertzian contact stress analysis for an elastic half-space normal and sliding contact. Int J Solids Struct 19(4):357–373CrossRefMATH
2.
Zurück zum Zitat Aleynikov S (2010) Spatial contact problems in geotechnics: boundary-element method. Springer, BerlinCrossRefMATH Aleynikov S (2010) Spatial contact problems in geotechnics: boundary-element method. Springer, BerlinCrossRefMATH
3.
Zurück zum Zitat Alliney S, Tralli A, Alessandri C (1990) Boundary variational formulations and numerical solution techniques for unilateral contact problems. Comput Mech 6(4):247–257CrossRefMATH Alliney S, Tralli A, Alessandri C (1990) Boundary variational formulations and numerical solution techniques for unilateral contact problems. Comput Mech 6(4):247–257CrossRefMATH
4.
Zurück zum Zitat Bazaraa MS, Sherali HD, Shetty CM (2013) Nonlinear programming: theory and algorithms. Wiley, LondonMATH Bazaraa MS, Sherali HD, Shetty CM (2013) Nonlinear programming: theory and algorithms. Wiley, LondonMATH
5.
Zurück zum Zitat Bemporad A, Paggi M (2015) Optimization algorithms for the solution of the frictionless normal contact between rough surfaces. Int J Solids Struct 69:94–105CrossRef Bemporad A, Paggi M (2015) Optimization algorithms for the solution of the frictionless normal contact between rough surfaces. Int J Solids Struct 69:94–105CrossRef
6.
Zurück zum Zitat Borodich FM, Keer LM (2004) Contact problems and depth-sensing nanoindentation for frictionless and frictional boundary conditions. Int J Solids Struct 41(9):2479–2499CrossRefMATH Borodich FM, Keer LM (2004) Contact problems and depth-sensing nanoindentation for frictionless and frictional boundary conditions. Int J Solids Struct 41(9):2479–2499CrossRefMATH
7.
Zurück zum Zitat Boussinesq J (1885) Application des potentiels à l’etude de l’équilibre et du mouvement des solides élastiques. Gauthier Villars, ParisMATH Boussinesq J (1885) Application des potentiels à l’etude de l’équilibre et du mouvement des solides élastiques. Gauthier Villars, ParisMATH
8.
Zurück zum Zitat Campos L, Oden J, Kikuchi N (1982) A numerical analysis of a class of contact problems with friction in elastostatics. Comput Methods Appl Mech Eng 34(1):821–845ADSMathSciNetCrossRefMATH Campos L, Oden J, Kikuchi N (1982) A numerical analysis of a class of contact problems with friction in elastostatics. Comput Methods Appl Mech Eng 34(1):821–845ADSMathSciNetCrossRefMATH
9.
Zurück zum Zitat Cerruti V (1882) Ricerche intorno all’equilibrio de’ corpi elastici isotropi. Reale Accademia de’ Lincei, Classe di Scienze Fisiche, Matematiche e Naturali 3(13):81–122 Cerruti V (1882) Ricerche intorno all’equilibrio de’ corpi elastici isotropi. Reale Accademia de’ Lincei, Classe di Scienze Fisiche, Matematiche e Naturali 3(13):81–122
10.
Zurück zum Zitat Conry TF, Seireg A (1971) A mathematical programming method for design of elastic bodies in contact. J Appl Mech 38:387–392CrossRef Conry TF, Seireg A (1971) A mathematical programming method for design of elastic bodies in contact. J Appl Mech 38:387–392CrossRef
12.
Zurück zum Zitat Corbett CJ, Sauer RA (2015) Three-dimensional isogeometrically enriched finite elements for frictional contact and mixed-mode debonding. Comput Methods Appl Mech Eng 284:781–806ADSMathSciNetCrossRef Corbett CJ, Sauer RA (2015) Three-dimensional isogeometrically enriched finite elements for frictional contact and mixed-mode debonding. Comput Methods Appl Mech Eng 284:781–806ADSMathSciNetCrossRef
13.
Zurück zum Zitat De Hosson JTM, Brebbia CA (2013) Surface effects and contact mechanics XI: computational methods and experiments, vol 78. Wit Press, AshurstCrossRef De Hosson JTM, Brebbia CA (2013) Surface effects and contact mechanics XI: computational methods and experiments, vol 78. Wit Press, AshurstCrossRef
14.
Zurück zum Zitat De Lorenzis L, Temizer I, Wriggers P, Zavarise G (2011) A large deformation frictional contact formulation using NURBS-based isogeometric analysis. Int J Numer Methods Eng 87(13):1278–1300MathSciNetMATH De Lorenzis L, Temizer I, Wriggers P, Zavarise G (2011) A large deformation frictional contact formulation using NURBS-based isogeometric analysis. Int J Numer Methods Eng 87(13):1278–1300MathSciNetMATH
16.
Zurück zum Zitat De Lorenzis L, Wriggers P, Zavarise G (2012) A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented lagrangian method. Comput Mech 49(1):1–20MathSciNetCrossRefMATH De Lorenzis L, Wriggers P, Zavarise G (2012) A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented lagrangian method. Comput Mech 49(1):1–20MathSciNetCrossRefMATH
17.
Zurück zum Zitat Dimitri R, De Lorenzis L, Scott MA, Wriggers P, Taylor RL, Zavarise G (2014) Isogeometric large deformation frictionless contact using T-splines. Comput Methods Appl Mech Eng 269:394–414ADSMathSciNetCrossRefMATH Dimitri R, De Lorenzis L, Scott MA, Wriggers P, Taylor RL, Zavarise G (2014) Isogeometric large deformation frictionless contact using T-splines. Comput Methods Appl Mech Eng 269:394–414ADSMathSciNetCrossRefMATH
18.
Zurück zum Zitat Dimitri R, De Lorenzis L, Wriggers P, Zavarise G (2014) NURBS-and T-spline-based isogeometric cohesive zone modeling of interface debonding. Comput Mech 54(2):369–388MathSciNetCrossRefMATH Dimitri R, De Lorenzis L, Wriggers P, Zavarise G (2014) NURBS-and T-spline-based isogeometric cohesive zone modeling of interface debonding. Comput Mech 54(2):369–388MathSciNetCrossRefMATH
20.
Zurück zum Zitat D’Urso M (2014) Analytical computation of gravity effects for polyhedral bodies. J Geodesy 88:13–29ADSCrossRef D’Urso M (2014) Analytical computation of gravity effects for polyhedral bodies. J Geodesy 88:13–29ADSCrossRef
21.
Zurück zum Zitat D’Urso MG (2012) New expressions of the gravitational potential and its derivates for the prism. In: Sneeuw N, Novák P, Crespi M, Sansò F (eds.) VII Hotine-Marussi international symposium on mathematical geodesy, Springer-Verlag, Berlin, pp 251–256 D’Urso MG (2012) New expressions of the gravitational potential and its derivates for the prism. In: Sneeuw N, Novák P, Crespi M, Sansò F (eds.) VII Hotine-Marussi international symposium on mathematical geodesy, Springer-Verlag, Berlin, pp 251–256
22.
Zurück zum Zitat D’Urso MG (2013) On the evaluation of the gravity effects of polyhedral bodies and a consistent treatment of related singularities. J Geodesy 87(3):239–252ADSCrossRef D’Urso MG (2013) On the evaluation of the gravity effects of polyhedral bodies and a consistent treatment of related singularities. J Geodesy 87(3):239–252ADSCrossRef
23.
24.
Zurück zum Zitat D’Urso MG (2015) A remark on the computation of the gravitational potential of masses with linearly varying density. In: VIII Hotine-Marussi symposium on mathematical geodesy, Springer, pp 205–212 D’Urso MG (2015) A remark on the computation of the gravitational potential of masses with linearly varying density. In: VIII Hotine-Marussi symposium on mathematical geodesy, Springer, pp 205–212
25.
Zurück zum Zitat D’Urso MG (2015) The gravity anomaly of a 2D polygonal body having density contrast given by polynomial functions. Surv Geophys 36(3):391–425ADSCrossRef D’Urso MG (2015) The gravity anomaly of a 2D polygonal body having density contrast given by polynomial functions. Surv Geophys 36(3):391–425ADSCrossRef
26.
Zurück zum Zitat D’Urso MG, Marmo F (2009) Vertical stresses due to linearly distributed pressures over polygonal domains. In: ComGeo I, first international symposium on computational geomechanics. Juan les Pins, France, pp 283–289 D’Urso MG, Marmo F (2009) Vertical stresses due to linearly distributed pressures over polygonal domains. In: ComGeo I, first international symposium on computational geomechanics. Juan les Pins, France, pp 283–289
27.
Zurück zum Zitat D’Urso MG, Marmo F (2013) On a generalized Love’s problem. Comput Geosci 61:144–151ADSCrossRef D’Urso MG, Marmo F (2013) On a generalized Love’s problem. Comput Geosci 61:144–151ADSCrossRef
28.
Zurück zum Zitat D’Urso MG, Marmo F (2015) Vertical stress distribution in isotropic half-spaces due to surface vertical loadings acting over polygonal domains. Zeitschrift für Angewandte Mathematik und Mechanik 95(1):91–110ADSMathSciNetCrossRefMATH D’Urso MG, Marmo F (2015) Vertical stress distribution in isotropic half-spaces due to surface vertical loadings acting over polygonal domains. Zeitschrift für Angewandte Mathematik und Mechanik 95(1):91–110ADSMathSciNetCrossRefMATH
29.
Zurück zum Zitat D’Urso MG, Russo P (2002) A new algorithm for point-in polygon test. Surv Rev 36(284):410–422CrossRef D’Urso MG, Russo P (2002) A new algorithm for point-in polygon test. Surv Rev 36(284):410–422CrossRef
30.
Zurück zum Zitat D’Urso MG, Trotta S (2015) Comparative assessment of linear and bilinear prism-based strategies for terrain correction computations. J Geodesy 89(3):199–215ADSCrossRef D’Urso MG, Trotta S (2015) Comparative assessment of linear and bilinear prism-based strategies for terrain correction computations. J Geodesy 89(3):199–215ADSCrossRef
31.
Zurück zum Zitat D’Urso MG, Trotta S (2017) Gravity anomaly of polihedral bodies having having a polynomial density contrast. Surv Geophys 38(4):781–832ADSCrossRef D’Urso MG, Trotta S (2017) Gravity anomaly of polihedral bodies having having a polynomial density contrast. Surv Geophys 38(4):781–832ADSCrossRef
32.
Zurück zum Zitat Dydo JR, Busby HR (1995) Elasticity solutions for constant and linearly varying load applied to a rectangular surface patch on the elastic half-space. J Elast 38(2):153–163MathSciNetCrossRefMATH Dydo JR, Busby HR (1995) Elasticity solutions for constant and linearly varying load applied to a rectangular surface patch on the elastic half-space. J Elast 38(2):153–163MathSciNetCrossRefMATH
33.
Zurück zum Zitat Eterovic A, Bathe K (1991) On the treatment of inequality constraints arising from contact conditions in finite element analysis. Comput Struct 40(2):203–209CrossRef Eterovic A, Bathe K (1991) On the treatment of inequality constraints arising from contact conditions in finite element analysis. Comput Struct 40(2):203–209CrossRef
34.
Zurück zum Zitat Gladwell GM (1980) Contact problems in the classical theory of elasticity. Springer, BerlinCrossRefMATH Gladwell GM (1980) Contact problems in the classical theory of elasticity. Springer, BerlinCrossRefMATH
35.
Zurück zum Zitat González JA, Park K, Felippa CA, Abascal R (2008) A formulation based on localized Lagrange multipliers for bem-fem coupling in contact problems. Comput Methods Appl Mech Eng 197(6):623–640ADSMathSciNetCrossRefMATH González JA, Park K, Felippa CA, Abascal R (2008) A formulation based on localized Lagrange multipliers for bem-fem coupling in contact problems. Comput Methods Appl Mech Eng 197(6):623–640ADSMathSciNetCrossRefMATH
36.
Zurück zum Zitat Goodman L (1962) Contact stress analysis of normally loaded rough spheres. ASME J Appl Mech 29(3):515–522 Goodman L (1962) Contact stress analysis of normally loaded rough spheres. ASME J Appl Mech 29(3):515–522
37.
Zurück zum Zitat Guyot N, Kosior F, Maurice G (2000) Coupling of finite elements and boundary elements methods for study of the frictional contact problem. Comput Methods Appl Mech Eng 181(1):147–159ADSCrossRefMATH Guyot N, Kosior F, Maurice G (2000) Coupling of finite elements and boundary elements methods for study of the frictional contact problem. Comput Methods Appl Mech Eng 181(1):147–159ADSCrossRefMATH
38.
Zurück zum Zitat Hartnett MJ (1980) A general numerical solution for elastic body contact problems. Solid Contact Lubr ASME AMD 39:51–66 Hartnett MJ (1980) A general numerical solution for elastic body contact problems. Solid Contact Lubr ASME AMD 39:51–66
39.
Zurück zum Zitat Hertz H (1882) On the contact of elastic solids. J. Reine und Angewandte Mathematik 92, 156–171 . (The date is often given wrongly as 1881) Hertz H (1882) On the contact of elastic solids. J. Reine und Angewandte Mathematik 92, 156–171 . (The date is often given wrongly as 1881)
40.
Zurück zum Zitat Hyun S, Pei L, Robbins MO (2004) Finite-element analysis of contact between elastic self-affine surfaces. Phys Rev E 70(2):026–117 Hyun S, Pei L, Robbins MO (2004) Finite-element analysis of contact between elastic self-affine surfaces. Phys Rev E 70(2):026–117
41.
42.
Zurück zum Zitat Kalker JJ, Van Randen Y (1972) A minimum principle for frictionless elastic contact with application to non-Hertzian half-space contact problems. J Eng Math 6(2):193–206MathSciNetCrossRefMATH Kalker JJ, Van Randen Y (1972) A minimum principle for frictionless elastic contact with application to non-Hertzian half-space contact problems. J Eng Math 6(2):193–206MathSciNetCrossRefMATH
44.
Zurück zum Zitat Kikuchi N, Oden JT (1988) Contact problems in elasticity: a study of variational inequalities and finite element methods. SANM, Philadelphia Kikuchi N, Oden JT (1988) Contact problems in elasticity: a study of variational inequalities and finite element methods. SANM, Philadelphia
45.
Zurück zum Zitat Kosior F, Guyot N, Maurice G (1999) Analysis of frictional contact problem using boundary element method and domain decomposition method. Int J Numer Methods Eng 46(1):65–82CrossRefMATH Kosior F, Guyot N, Maurice G (1999) Analysis of frictional contact problem using boundary element method and domain decomposition method. Int J Numer Methods Eng 46(1):65–82CrossRefMATH
46.
Zurück zum Zitat Li J, Berger EJ (2001) A boussinesq-cerruti solution set for constant and linear distribution of normal and tangential load over a triangular area. J Elast 63(2):137–151MathSciNetCrossRefMATH Li J, Berger EJ (2001) A boussinesq-cerruti solution set for constant and linear distribution of normal and tangential load over a triangular area. J Elast 63(2):137–151MathSciNetCrossRefMATH
47.
Zurück zum Zitat Li J, Berger EJ (2003) A semi-analytical approach to three-dimensional normal contact problems with friction. Comput Mech 30(4):310–322CrossRefMATH Li J, Berger EJ (2003) A semi-analytical approach to three-dimensional normal contact problems with friction. Comput Mech 30(4):310–322CrossRefMATH
48.
49.
Zurück zum Zitat Love AEH (1929) The stress produced in a semi-infinite solid by pressure on part of the boundary. Philos Trans R Soc Lond 228:377–420ADSCrossRefMATH Love AEH (1929) The stress produced in a semi-infinite solid by pressure on part of the boundary. Philos Trans R Soc Lond 228:377–420ADSCrossRefMATH
50.
Zurück zum Zitat Marmo F, Rosati L (2016) A general approach to the solution of Boussinesq’s problem for polynomial pressures acting over polygonal domains. J Elast 122:75–112MathSciNetCrossRefMATH Marmo F, Rosati L (2016) A general approach to the solution of Boussinesq’s problem for polynomial pressures acting over polygonal domains. J Elast 122:75–112MathSciNetCrossRefMATH
51.
Zurück zum Zitat Marmo F, Sessa S, Rosati L (2016) Analytical solution of the Cerruti problem under linearly distributed horizontal pressures over polygonal domains. J Elast 124:27–56CrossRefMATH Marmo F, Sessa S, Rosati L (2016) Analytical solution of the Cerruti problem under linearly distributed horizontal pressures over polygonal domains. J Elast 124:27–56CrossRefMATH
52.
Zurück zum Zitat Marmo F, Toraldo F, Rosati L (2016) Analytical formulas and design charts for transversely isotropic half-spaces subject to linearly distributed pressures. Meccanica 51(11):2909–2928MathSciNetCrossRef Marmo F, Toraldo F, Rosati L (2016) Analytical formulas and design charts for transversely isotropic half-spaces subject to linearly distributed pressures. Meccanica 51(11):2909–2928MathSciNetCrossRef
53.
Zurück zum Zitat Marmo F, Toraldo F, Rosati L (2017) Transversely isotropic half-spaces subject to surface pressures. Int J Solids Struct 104:35–49CrossRef Marmo F, Toraldo F, Rosati L (2017) Transversely isotropic half-spaces subject to surface pressures. Int J Solids Struct 104:35–49CrossRef
54.
Zurück zum Zitat Matzen ME, Cichosz T, Bischoff M (2013) A point to segment contact formulation for isogeometric, NURBS based finite elements. Comput Methods Appl Mech Eng 255:27–39ADSMathSciNetCrossRefMATH Matzen ME, Cichosz T, Bischoff M (2013) A point to segment contact formulation for isogeometric, NURBS based finite elements. Comput Methods Appl Mech Eng 255:27–39ADSMathSciNetCrossRefMATH
55.
Zurück zum Zitat Mossakovskii V (1954) The fundamental mixed problem of the theory of elasticity for a half-space with a circular line separating the boundary conditions. Prikladnaya Matematika i Mekhanika 18(2):187–196MathSciNet Mossakovskii V (1954) The fundamental mixed problem of the theory of elasticity for a half-space with a circular line separating the boundary conditions. Prikladnaya Matematika i Mekhanika 18(2):187–196MathSciNet
56.
Zurück zum Zitat Nogi T, Kato T (1998) Influence of a hard surface layer on the limit of elastic contact—Part I: Analysis using a real surface model. J Tribol 110:493–500 Nogi T, Kato T (1998) Influence of a hard surface layer on the limit of elastic contact—Part I: Analysis using a real surface model. J Tribol 110:493–500
57.
Zurück zum Zitat Paggi M, Ciavarella M (2010) The coefficient of proportionality \(\kappa \) between real contact area and load, with new asperity models. Wear 268(7):1020–1029CrossRef Paggi M, Ciavarella M (2010) The coefficient of proportionality \(\kappa \) between real contact area and load, with new asperity models. Wear 268(7):1020–1029CrossRef
58.
Zurück zum Zitat Pantuso D, Bathe KJ, Bouzinov PA (2000) A finite element procedure for the analysis of thermo-mechanical solids in contact. Comput Struct 75(6):551–573CrossRef Pantuso D, Bathe KJ, Bouzinov PA (2000) A finite element procedure for the analysis of thermo-mechanical solids in contact. Comput Struct 75(6):551–573CrossRef
59.
Zurück zum Zitat Paris F, Garrido J (1989) An incremental procedure for friction contact problems with the boundary element method. Eng Anal Bound Elements 6(4):202–213CrossRef Paris F, Garrido J (1989) An incremental procedure for friction contact problems with the boundary element method. Eng Anal Bound Elements 6(4):202–213CrossRef
60.
Zurück zum Zitat Pohrt R, Li Q (2014) Complete boundary element formulation for normal and tangential contact problems. Phys Mesomech 17(4):334–340CrossRef Pohrt R, Li Q (2014) Complete boundary element formulation for normal and tangential contact problems. Phys Mesomech 17(4):334–340CrossRef
61.
Zurück zum Zitat Pohrt R, Popov VL, Filippov AE (2012) Normal contact stiffness of elastic solids with fractal rough surfaces for one-and three-dimensional systems. Phys Rev E 86(2):026–710 Pohrt R, Popov VL, Filippov AE (2012) Normal contact stiffness of elastic solids with fractal rough surfaces for one-and three-dimensional systems. Phys Rev E 86(2):026–710
62.
Zurück zum Zitat Polonsky IA, Keer LM (1999) A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques. Wear 231(2):206–219CrossRef Polonsky IA, Keer LM (1999) A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques. Wear 231(2):206–219CrossRef
63.
Zurück zum Zitat Polonsky IA, Keer LM (2000) A fast and accurate method for numerical analysis of elastic layered contacts. ASME J Tribol 122:30–35CrossRef Polonsky IA, Keer LM (2000) A fast and accurate method for numerical analysis of elastic layered contacts. ASME J Tribol 122:30–35CrossRef
64.
Zurück zum Zitat Polonsky IA, Keer LM (2000) Fast methods for solving rough contact problems: a comparative study. ASME J Tribol 122(1):36–41CrossRef Polonsky IA, Keer LM (2000) Fast methods for solving rough contact problems: a comparative study. ASME J Tribol 122(1):36–41CrossRef
65.
Zurück zum Zitat Popov V (2010) Contact mechanics and friction: physical principles and applications. Springer, BerlinCrossRefMATH Popov V (2010) Contact mechanics and friction: physical principles and applications. Springer, BerlinCrossRefMATH
66.
Zurück zum Zitat Prodanov N, Dapp WB, Müser MH (2014) On the contact area and mean gap of rough, elastic contacts: Dimensional analysis, numerical corrections, and reference data. Tribol Lett 53(2):433–448CrossRef Prodanov N, Dapp WB, Müser MH (2014) On the contact area and mean gap of rough, elastic contacts: Dimensional analysis, numerical corrections, and reference data. Tribol Lett 53(2):433–448CrossRef
67.
Zurück zum Zitat Putignano C, Afferrante L, Carbone G, Demelio G (2012) A new efficient numerical method for contact mechanics of rough surfaces. Int J Solids Struct 49(2):338–343CrossRef Putignano C, Afferrante L, Carbone G, Demelio G (2012) A new efficient numerical method for contact mechanics of rough surfaces. Int J Solids Struct 49(2):338–343CrossRef
68.
Zurück zum Zitat Rosati L, Marmo F (2014) A closed form expression of the thermo-mechanical fields induced by a uniform heat source acting over an isotropic half-space. Int J Heat Mass Transf 75:272–283CrossRef Rosati L, Marmo F (2014) A closed form expression of the thermo-mechanical fields induced by a uniform heat source acting over an isotropic half-space. Int J Heat Mass Transf 75:272–283CrossRef
69.
Zurück zum Zitat Russ JC (1994) Hurst and Fourier analysis. In: Fractal surfaces, Springer, New York, pp 83–114 Russ JC (1994) Hurst and Fourier analysis. In: Fractal surfaces, Springer, New York, pp 83–114
70.
Zurück zum Zitat Sackfield A, Hills D, Nowell D (2013) Mechanics of elastic contacts. Elsevier, AmsterdamMATH Sackfield A, Hills D, Nowell D (2013) Mechanics of elastic contacts. Elsevier, AmsterdamMATH
71.
Zurück zum Zitat Simo JC, Laursen T (1992) An augmented Lagrangian treatment of contact problems involving friction. Comput Struct 42(1):97–116MathSciNetCrossRefMATH Simo JC, Laursen T (1992) An augmented Lagrangian treatment of contact problems involving friction. Comput Struct 42(1):97–116MathSciNetCrossRefMATH
72.
Zurück zum Zitat Singh KP, Paul B (1974) Numerical solution of non-Hertzian elastic contact problems. J Appl Mech 41(2):484–490CrossRef Singh KP, Paul B (1974) Numerical solution of non-Hertzian elastic contact problems. J Appl Mech 41(2):484–490CrossRef
73.
Zurück zum Zitat Spence D (1968) Self similar solutions to adhesive contact problems with incremental loading. In: Proceedings of the royal society of London A: mathematical, physical and engineering sciences, vol 305, The Royal Society pp 55–80 Spence D (1968) Self similar solutions to adhesive contact problems with incremental loading. In: Proceedings of the royal society of London A: mathematical, physical and engineering sciences, vol 305, The Royal Society pp 55–80
74.
Zurück zum Zitat Svec OJ, Gladwell GML (1971) An explicit Boussinesq solution for a polynomial distribution of pressure over a triangular region. J Elast 1:167–170CrossRef Svec OJ, Gladwell GML (1971) An explicit Boussinesq solution for a polynomial distribution of pressure over a triangular region. J Elast 1:167–170CrossRef
75.
Zurück zum Zitat Temizer I, Wriggers P, Hughes TJR (2011) Contact treatment in isogeometric analysis with NURBS. Comput Methods Appl Mech Eng 200(9–12):1100–1112ADSMathSciNetCrossRefMATH Temizer I, Wriggers P, Hughes TJR (2011) Contact treatment in isogeometric analysis with NURBS. Comput Methods Appl Mech Eng 200(9–12):1100–1112ADSMathSciNetCrossRefMATH
76.
Zurück zum Zitat Trotta S, Marmo F, Rosati L (2016) Analytical expression of the eshelby tensor for arbitrary polygonal inclusions in two-dimensional elasticity. Compos B Eng 106:48–58CrossRef Trotta S, Marmo F, Rosati L (2016) Analytical expression of the eshelby tensor for arbitrary polygonal inclusions in two-dimensional elasticity. Compos B Eng 106:48–58CrossRef
77.
Zurück zum Zitat Trotta S, Marmo F, Rosati L (2017) Evaluation of the eshelby tensor for polygonal inclusions. Compos B Eng 115:170–181CrossRef Trotta S, Marmo F, Rosati L (2017) Evaluation of the eshelby tensor for polygonal inclusions. Compos B Eng 115:170–181CrossRef
78.
Zurück zum Zitat Vijayaker S, Busby H, Wilcox L (1989) Finite element analysis of three-dimensional conformal contact with friction. Comput Struct 33(1):49–61CrossRefMATH Vijayaker S, Busby H, Wilcox L (1989) Finite element analysis of three-dimensional conformal contact with friction. Comput Struct 33(1):49–61CrossRefMATH
79.
80.
Zurück zum Zitat Wriggers P, Simo J (1985) A note on tangent stiffness for fully nonlinear contact problems. Commun Appl Numer Methods 1(5):199–203CrossRefMATH Wriggers P, Simo J (1985) A note on tangent stiffness for fully nonlinear contact problems. Commun Appl Numer Methods 1(5):199–203CrossRefMATH
81.
Zurück zum Zitat Wriggers P, Zavarise G (1993) Application of augmented Lagrangian techniques for non-linear constitutive laws in contact interfaces. Commun Numer Methods Eng 9(10):815–824CrossRefMATH Wriggers P, Zavarise G (1993) Application of augmented Lagrangian techniques for non-linear constitutive laws in contact interfaces. Commun Numer Methods Eng 9(10):815–824CrossRefMATH
82.
Zurück zum Zitat Zavarise G, De Lorenzis L (2012) An augmented Lagrangian algorithm for contact mechanics based on linear regression. Int J Numer Methods Eng 91(8):825–842MathSciNetCrossRef Zavarise G, De Lorenzis L (2012) An augmented Lagrangian algorithm for contact mechanics based on linear regression. Int J Numer Methods Eng 91(8):825–842MathSciNetCrossRef
83.
Zurück zum Zitat Zavarise G, Wriggers P, Schrefler B (1995) On augmented Lagrangian algorithms for thermomechanical contact problems with friction. Int J Numer Methods Eng 38(17):2929–2949CrossRefMATH Zavarise G, Wriggers P, Schrefler B (1995) On augmented Lagrangian algorithms for thermomechanical contact problems with friction. Int J Numer Methods Eng 38(17):2929–2949CrossRefMATH
84.
Zurück zum Zitat Zhong ZH (1993) Finite element procedures for contact-impact problems. Oxford University Press, Oxford Zhong ZH (1993) Finite element procedures for contact-impact problems. Oxford University Press, Oxford
Metadaten
Titel
Numerical solution of smooth and rough contact problems
verfasst von
Francesco Marmo
Ferdinando Toraldo
Alessandra Rosati
Luciano Rosati
Publikationsdatum
09.10.2017
Verlag
Springer Netherlands
Erschienen in
Meccanica / Ausgabe 6/2018
Print ISSN: 0025-6455
Elektronische ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-017-0766-2

Weitere Artikel der Ausgabe 6/2018

Meccanica 6/2018 Zur Ausgabe

Novel Computational Approaches to Old and New Problems in Mechanics

A phase-field approach to conchoidal fracture

Novel Computational Approaches to Old and New Problems in Mechanics

Blade cutting of thin walled structures by explicit dynamics finite elements

Novel Computational Approaches to Old and New Problems in Mechanics

Asymptotic homogenization of fibre-reinforced composites: a virtual element method approach

Novel Computational Approaches to Old and New Problems in Mechanics

Mixed isogeometric collocation methods for the simulation of poromechanics problems in 1D

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.