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1996 | 37 | 1 | 343-349
Tytuł artykułu

Mixed formulation for elastic problems - existence, approximation, and applications to Poisson structures

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A mixed formulation is given for elastic problems. Existence and uniqueness of the discretized problem are given for conformal continuous interpolations for the stress tensor components and for the components of the displacement vector. A counterpart of the problem is discussed in the case of an even-dimensional Euclidean space with an associated Hamiltonian vector field and the Poisson structure. For conformal interpolations of the same order the question remains open.
Słowa kluczowe
Rocznik
Tom
37
Numer
1
Strony
343-349
Opis fizyczny
Daty
wydano
1996
Twórcy
  • Institute of Mathematics, Polish Academy of Sciences, Narutowicza 56, PL-90-136 Łodź, Poland
  • Laboratoire d'Analyse Numérique, Université de Rennes, 1, Avenue du Général Leclerc, F-35000 Rennes, France
  • Department of Mathematics, University of Athens, Panepistimiopolis, GR-15784 Athens, Greece
autor
  • École Nationale d'Ingénieurs, 58, Rue Jean Parrot, F-42023 Saint-Étienne, France
Bibliografia
  • [1] R. Friat, Contribution à la modélisation par éléments finis du problème de contact avec frottement et de l'indentation d'un bicouche, en comportement élasto-plastique parfait, Thèse de Mécanique, Université de Nantes, 1994.
  • [2] M. Fukushima, Y. Oshima and M. Takeda, Dirichlet Forms and Symmetric Markov Processes, Walter de Gruyter Studies in Mathematics 19, W. de Gruyter, Berlin-New York 1994.
  • [3] B. Gaveau et J. Ławrynowicz, Espaces de Dirichlet invariants biholomorphes et capacités associées, Bull. Acad. Polon. Sci. Sér. Sci. Math. 30 (1982), 63-69.
  • [4] B. Gaveau, J. Ławrynowicz, et L. Wojtczak, Equations de Langevin generalisées dans les milieux inhomogènes, C. R. Acad. Sci. Paris Sér. I 296 (1983), 411-413.
  • [5] V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms, Springer Series in Computational Matematics, Springer, Berlin 1986.
  • [6] A. A. Kirillov, Elements of the Theory of Representations, Springer, New York 1976.
  • [7] P. Labé, Étude de structures stratifiées en comportement élasto-plastique par des éléments finis mixtes, Thèse de Docteur Ingénieur - Université de Rennes, 1980.
  • [8] J. Ławrynowicz, J. Kalina and M. Okada, Foliations by complex manifolds involving the complex hessian, (a) Ninth Conf. Analytic Functions Abstracts, Lublin 1986, pp. 29-30 (abstract), (b) Inst. of Math. Polish Acad. Sci. Preprint no. 486 (1991), ii + 40 pp., (c) Dissertationes Math. 331 (1994), 45 pp.
  • [9] J. Ławrynowicz and M. Okada, Canonical diffusion and foliation involving the complex hessian, (a) Inst. of Math. Polish Acad. Sci. Preprint no. 356 (1985), ii + 10 pp., (b) Bull. Polish Acad. Sci. Math. 34 (1986), 661-667.
  • [10] J. Ławrynowicz, J. Rembieliński and F. Succi, Generalized Hurwitz maps of the type S × V → W, anti-involutions, and quantum braided Clifford algebras, this volume, 223-240.
  • [11] J. Ławrynowicz and L. Wojtczak in cooperation with S. Koshi and O. Suzuki, Stochastical mechanics of particle systems in Clifford-analytical formulation related to Hurwitz pairs of dimension (8,5), in: Deformations of Mathematical Structures II. Hurwitz-Type Structures and Applications to Surface Physics, J. Ławrynowicz (ed.), Kluwer Academic Publishers, Dordrecht-Boston-London 1994, pp. 213-262.
  • [12] A. Lichnerowicz, Les variétés de Poisson et leur algèbres de Lie associées, J. Diff. Geom. 12 (1977), 253-300.
  • [13] A. Lichnerowicz, Variétés de Poisson et feuilletages, Ann. Fac. Sci. Toulouse Math. (5) 4 (1982), 195-262.
  • [14] G. Lube, Stabilized Galerkin finite element methods for convection dominated and incompressible flow problems, in: Numerical Analysis and Mathematical Modelling, J.K. Kowalski and A. Wakulicz (eds.), Banach Center Publications, 29 Pol. Acad. Sci. - Inst. of Math., Warszawa 1994, pp. 85-104.
  • [15] A.-L. Mignot and C. Surry, A mixed finite element family in plane elasticity, Appl. Math. Mod. 5 (1981), 259-262.
  • [16] S. Nečas and I. Hlavaček, Mathematical Theory of Elastic and Elasto-Plastic Bodies - An Introduction, Elsevier, Amsterdam 1981.
  • [17] P. J. Olver, Applications of Lie Groups to Differential Equations, Graduate Texts in Mathematics 107, Springer, New York-Berlin-Heidelberg-Tokyo 1986.
  • [18] L. C. Papaloucas, Polynomial Poisson subalgebras, Bull. Soc. Sci. Lettres Łódź 45, Sér. Rech. Déform. 19 (1995), 57-64.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv37i1p343bwm
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