Publication Cover
Applicable Analysis
An International Journal
Volume 90, 2011 - Issue 2
69
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Contact problems with friction for hemitropic solids: boundary variational inequality approach

, , &
Pages 279-303 | Received 13 Feb 2010, Accepted 27 Jun 2010, Published online: 07 Dec 2010

References

  • Cosserat , E and Cosserat , F . 1898 . Sur les equations de la theorie de l'elasticite . C.R. Acad. Sci. Paris , 126 : 1129 – 1132 .
  • Cosserat , E and Cosserat , F . 1909 . Théorie des Corps Deformables , Paris : Herman .
  • Dyszlewicz , J . 2004 . Micropolar Theory of Elasticity, Lecture Notes in Applied and Computational Mechanics , Vol. 15 , Berlin : Springer-Verlag .
  • Kupradze , VD , Gegelia , TG , Basheleishvili , MO and Burchuladze , TV . 1976 . Three Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity (in Russian) , Moscow : Nauka . (English translation: North Holland Series in Applied Mathematics and Mechanics, Vol. 25, North-Holland, Amsterdam, New York, Oxford, 1979)
  • Mindlin , RD . 1964 . Micro-structure in linear elasticity . Arch. Ration. Mech. Anal. , 16 : 51 – 78 .
  • Nowacki , W . 1986 . Theory of Asymmetric Elasticity , Oxford : Pergamon Press . PWN/Polish Scientific Publishers, Warsaw
  • Aero , EL and Kuvshinski , EV . 1963 . Continuum theory of asymmetric elasticity. Microrotation effect . Solid State Phys. , 5 ( 9 ) : 2591 – 2598 . (in Russian), (English translation: Soviet Phys. – Solid State 5 (1964), pp. 1892–1899)
  • Aero , EL and Kuvshinski , EV . 1964 . Continuum theory of asymmetric elasticity. Equilibrium of an isotropic body . Solid State Phys. , 6 ( 9 ) : 2689 – 2699 . (in Russian), (English translation: Soviet Phys. – Solid State 6 (1965), pp. 2141–2148)
  • Eringen , AC . 1999 . Microcontinuum Field Theories: I. Foundations and Solids , New York : Springer-Verlag .
  • Haijun , Z and Zhong-can , O . 1998 . Bending and twisting elasticity: A revised Marko-Sigga model on DNA chirality . Phys. Rev. E , 58 ( 4 ) : 4816 – 4821 .
  • Lakes , RS . 2001 . Elastic and viscoelastic behavior of chiral materials . Int. J. Mech. Sci. , 43 : 1579 – 1589 .
  • Lakes , RS and Benedict , RL . 1982 . Noncentrosymmetry in micropolar elasticity . Int. J. Eng. Sci. , 29 : 1161 – 1167 .
  • Mura , T . 1987 . Micromechanics of Defects in Solids , Hague, , The Netherlands : Martinus Nijhoff .
  • Mura , T . 2000 . Some new problems in the micromechanics . Mater. Sci. Eng. A (Struct. Mater.: Properties, Microstruct. Process.) , A285 ( 1–2 ) : 224 – 228 .
  • Ro , R . 1999 . Elastic activity of the chiral medium . J. Appl. Phys. , 85 : 2508 – 2513 .
  • Sharma , P . 2004 . Size-dependent elastic fields of embedded inclusions in isotropic chiral solids . Int. J. Solid. Struct. , 41 : 6317 – 6333 .
  • Yang , JFC and Lakes , RS . 1982 . Experimental study of micropolar and couple stress elasticity in compact bone bending . J. Biomech. , 15 : 91 – 98 .
  • Natroshvili , D , Gachechiladze , R , Gachechiladze , A and Stratis , I . 2007 . Transmission problems in the theory of elastic hemitropic materials . Appl. Anal. , 86 : 1463 – 1508 .
  • Natroshvili , D , Giorgashvili , L and Stratis , IG . 2003 . Mathematical problems of the theory of elasticity of chiral materials . Appl. Math. Inform. Mech. , 8 ( 1 ) : 47 – 103 .
  • Natroshvili , D , Giorgashvili , L and Zazashvili , S . 2005 . Steady state oscillation problems of the theory of elasticity of chiral materials . J. Int. Eqns Appl. , 17 : 19 – 69 .
  • Natroshvili , D and Stratis , IG . 2006 . Mathematical problems of the theory of elasticity of chiral materials for Lipschitz domains . Math. Meth. Appl. Sci. , 29 : 445 – 478 .
  • Elphinstone , MJ and Lakhtakia , A . 1994 . Plane-wave representation of an elastic chiral solid slab sand-wiched between achiral solid half-spaces . J. Acoust. Soc. Am. , 95 : 617 – 627 .
  • Lakhtakia , A , Varadan , VK and Varadan , VV . 1988 . Elastic wave propagation in noncentrosymmetric isotropic media: Dispersion and field equations . J. Appl. Phys. , 64 : 5246 – 5250 .
  • Lakhtakia , A , Varadan , VV and Varadan , VK . 1992 . Elastic wave scattering by an isotropic noncentrosymmetric sphere . J. Acoust. Soc. Am. , 91 : 680 – 684 .
  • Nowacki , JP . 1977 . Green function for a hemitropic micropolar continuum . Bull. Acad. Polon. Sci., Sér. Sci. Technol. , 25 : 235 – 241 .
  • Nowacki , JP and Nowacki , W . 1977 . Some problems of hemitropic micropolar continuum . Bull. Acad. Polon. Sci., Sér. Sci. Technol. , 25 : 151 – 159 .
  • Weitsman , Y . 1967 . Initial stress and skin effects in a hemitropic Cosserat continuum . J. Appl. Math. , 349 : 160 – 164 .
  • Gachechiladze , R , Gwinner , J and Natroshvili , D . 2006 . A boundary variational inequality approach to unilateral contact with hemitropic materials . Mem. Differ. Eqns Math. Phys. , 39 : 69 – 103 .
  • Duvaut , G and Lions , J-L . 1976 . Inequalities in Mechanics and Physics , Berlin : Springer-Verlag .
  • Eck , C , Jaruček , J and Krbec , M . 2005 . Unilateral Contact problems: Variational Methods and Existence Theorems , Doca Raton, FL : Chapman & Hall/CRC .
  • Fichera , G . 1963–1964 . Problemi elastostatici con vincoli unilaterali: Il problema di Signorini com ambigue condi-cioni al contorno . Accad. Naz. Lincei , 8 : 91 – 140 .
  • Fichera , G . 1972 . “ Boundary value problems of elasticity with unilateral constraints ” . In Handbuch der Physik, Bd. VIa/2: Mechanics of Solid II , Edited by: Truesdell , C . 391 – 424 . Berlin : Springer-Verlag .
  • Gachechiladze , A and Natroshvili , D . 2001 . Boundary variational inequality approach in the anisotropic elasticity for the Signorini problem . Georgian Math. J. , 8 : 462 – 692 .
  • Gwinner , J and Stephan , EP . 1993 . A boundary element procedure for contact problems in plane linear elastostatics . RAIRO Math. Model. Numer. Anal. , 27 : 457 – 480 .
  • H. Han and G.C. Hsiao, The boundary element method for a contact problem, in Theory and Applications of Boundary Element Methods, Proceedings of the 2nd China/Japan Symposium, Beijing, 1988, 1990, pp. 33–38.
  • Han , H . 1994 . A boundary element procedure for the Signorini problem in three–dimensional elasticity . Numer. Math., A J. Chin. Univ. , 3 ( 1 ) : 104 – 117 .
  • Hlaváček , I , Haslinger , J , Nečas , J and Loviček , J . 1983 . Solution of Variational Inequalities in Mechanics , Prague : SNTL .
  • Kikuchi , N and Oden , JT . 1988 . Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods , Philadelphia : SIAM .
  • Rodrigues , J-F . 1987 . Obstacle Problems in Mathematical Physics , Amsterdam : North-Holland .
  • Shillor , M , Sofonea , M and Telega , JJ . 2004 . Models and Analysis of Quasistatic Contact: Variational Methods , Berlin : Springer-Verlag .
  • Eck , C and Jaruček , J . 2000 . Existence results for the semicoercive static contact problem with Coulomb friction . Nonlinear Anal. Theor. Methods Appl. , 42 ( 6(A) : 961 – 976 .
  • Goeleven , D . 1996 . On Noncoercive Variational Problems and Related Results, Research Notes in Mathematics , Vol. 357 , Essex, , UK : Addison Wesley Longman .
  • Goeleven , D and Gwinner , J . 2002 . On semicoerciveness, a class of variational inequalities, and an application to von Kármán plates . Math. Nachr. , 244 : 89 – 109 .
  • Triebel , H . 1978 . Interpolation Theory, Function Spaces, Differential Operators , Amsterdam : North-Holland .
  • Fichera , G . 1972 . “ Existence Theorems in Elasticity ” . In Handbuch der Physik, Bd. VIa/2: Mechanics of Solid II , Edited by: Truesdell , C . 347 – 389 . Berlin : Springer-Verlag .
  • Ciarlet , PG . 1988 . Mathematical Elasticity , Vol. I , Amsterdam : North-Holland .
  • Lions , J-L and Magenes , E . 1972 . Non-homogeneous Boundary Value Problems and Applications, Vol. I (Die Grundlehren der mat. Wissenschaften, Band 181) , Berlin, Heidelberg, New York : Springer-Verlag .
  • Nečas , J . 1967 . Méthodes Directes en Théorie des Équations Élliptiques , Paris : Masson Éditeur .
  • Panagiotopoulos , PD . 1975 . A nonlinear programming approach to the unilateral contact- and friction-boundary value problems in the theory of elasticity . Ing. Arch. , 44 : 421 – 432 .
  • Haslinger , J , Kučera , R and Dostál , Z . 2004 . An algorithm for the numerical realization of 3D contact problems with Coulomb friction . J. Comput. Appl. Math. , 164–165 : 387 – 408 .
  • Nikolski , SM . 1969 . Approximation of Functions of Many Variables and Imbedding Theorems , Moscow : Nauka .
  • Glowinski , R , Lions , JL and Tremolieres , R . 1981 . Numerical Analysis of Variational Inequalities , Amsterdam : North-Holland .
  • Iskovskikh , VA . 2001 . “ Ruled Surface ” . In Encyclopaedia of Mathematics , Edited by: Hazewinkel , M . Norwell : Kluwer Academic .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.