Mixed formulation for elastic problems - existence, approximation, and applications to Poisson structures
Julian Ławrynowicz; Alain Mignot; Loucas Papaloucas; Claude Surry
Banach Center Publications (1996)
- Volume: 37, Issue: 1, page 343-349
- ISSN: 0137-6934
Access Full Article
topAbstract
topHow to cite
topŁawrynowicz, Julian, et al. "Mixed formulation for elastic problems - existence, approximation, and applications to Poisson structures." Banach Center Publications 37.1 (1996): 343-349. <http://eudml.org/doc/208612>.
@article{Ławrynowicz1996,
abstract = {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.},
author = {Ławrynowicz, Julian, Mignot, Alain, Papaloucas, Loucas, Surry, Claude},
journal = {Banach Center Publications},
keywords = {discretized problem; conformal continuous interpolation; stress tensor; displacement vector; even-dimensional Euclidean space; Hamiltonian vector field},
language = {eng},
number = {1},
pages = {343-349},
title = {Mixed formulation for elastic problems - existence, approximation, and applications to Poisson structures},
url = {http://eudml.org/doc/208612},
volume = {37},
year = {1996},
}
TY - JOUR
AU - Ławrynowicz, Julian
AU - Mignot, Alain
AU - Papaloucas, Loucas
AU - Surry, Claude
TI - Mixed formulation for elastic problems - existence, approximation, and applications to Poisson structures
JO - Banach Center Publications
PY - 1996
VL - 37
IS - 1
SP - 343
EP - 349
AB - 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.
LA - eng
KW - discretized problem; conformal continuous interpolation; stress tensor; displacement vector; even-dimensional Euclidean space; Hamiltonian vector field
UR - http://eudml.org/doc/208612
ER -
References
top- [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. Zbl0494.32002
- [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. Zbl0585.65077
- [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. Zbl0616.32018
- [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. Zbl0874.46012
- [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. Zbl0828.60081
- [12] A. Lichnerowicz, Les variétés de Poisson et leur algèbres de Lie associées, J. Diff. Geom. 12 (1977), 253-300. Zbl0405.53024
- [13] A. Lichnerowicz, Variétés de Poisson et feuilletages, Ann. Fac. Sci. Toulouse Math. (5) 4 (1982), 195-262. Zbl0517.58029
- [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. Zbl0801.76046
- [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. Zbl0448.73009
- [17] P. J. Olver, Applications of Lie Groups to Differential Equations, Graduate Texts in Mathematics 107, Springer, New York-Berlin-Heidelberg-Tokyo 1986. Zbl0588.22001
- [18] L. C. Papaloucas, Polynomial Poisson subalgebras, Bull. Soc. Sci. Lettres Łódź 45, Sér. Rech. Déform. 19 (1995), 57-64.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.