[Sur la formulation géométriquement exacte de la mécanique des structures et ses applications en dynamique, contrôle et optimisation]
Dans cet article nous réexaminons la formulation théorique de la mécanique des structures n'imposant aucune restriction sur la grandeur des déplacements, des rotations ou des déformations, qui est alors dite géométriquement exacte. Une attention pariculière est portée aux aspects du calcul pertinents aux rotations finies, dont la maı̂trise représente un élément clé pour toute formulation de ce type. Nous présentons brièvement quelques applications nouvelles de le théorie géométriquement exacte en dynamique, en contrôle et en optimisation.
In this survey paper we re-examine the theoretical formulation of structural mechanics, introducing no restrictions with respect to the size of displacements, rotations or deformations, which is commonly referred to as geometrically exact. A special attention is given to clarifying the computational aspects of finite rotations as the key ingredient of any such formulation. We briefly discuss several novel applications of the geometrically exact formulation to dynamics, control and optimization.
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Mot clés : Solides et structures, Rotation finie, Dynamique, Contrôle, Optimisation
Adnan Ibrahimbegovic 1
@article{CRMECA_2003__331_5_383_0,
author = {Adnan Ibrahimbegovic},
title = {On the geometrically exact formulation of structural mechanics and its applications to dynamics, control and optimization},
journal = {Comptes Rendus. M\'ecanique},
pages = {383--394},
publisher = {Elsevier},
volume = {331},
number = {5},
year = {2003},
doi = {10.1016/S1631-0721(03)00062-7},
language = {en},
}
TY - JOUR AU - Adnan Ibrahimbegovic TI - On the geometrically exact formulation of structural mechanics and its applications to dynamics, control and optimization JO - Comptes Rendus. Mécanique PY - 2003 SP - 383 EP - 394 VL - 331 IS - 5 PB - Elsevier DO - 10.1016/S1631-0721(03)00062-7 LA - en ID - CRMECA_2003__331_5_383_0 ER -
%0 Journal Article %A Adnan Ibrahimbegovic %T On the geometrically exact formulation of structural mechanics and its applications to dynamics, control and optimization %J Comptes Rendus. Mécanique %D 2003 %P 383-394 %V 331 %N 5 %I Elsevier %R 10.1016/S1631-0721(03)00062-7 %G en %F CRMECA_2003__331_5_383_0
Adnan Ibrahimbegovic. On the geometrically exact formulation of structural mechanics and its applications to dynamics, control and optimization. Comptes Rendus. Mécanique, Volume 331 (2003) no. 5, pp. 383-394. doi : 10.1016/S1631-0721(03)00062-7. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00062-7/
[1] Fundamentals of Structural Mechanics, Prentice-Hall, New York, 1997
[2] Finite Element Procedures, Prentice-Hall, New Jersey, 1996
[3] Nonlinear Finite Element Analysis of Solids and Structures, Wiley, 1997
[4] On finite deformations of space-curved beams, J. Appl. Math. Phys., Volume 32 (1981), pp. 734-744
[5] A finite-strain beam formulation. The three-dimensional dynamic problem. Part I, Comput. Methods Appl. Mech. Engrg., Volume 49 (1985), pp. 55-70
[6] Finite element implementation of Reissner's geometrically nonlinear beam theory: three-dimensional curved beam finite elements, Comput. Methods Appl. Mech. Engrg., Volume 122 (1995), pp. 10-26
[7] Stress resultant geometrically nonlinear shell theory with drilling rotations. Part 1: A consistent formulation, Comput. Methods Appl. Mech. Engrg., Volume 118 (1994), pp. 265-284
[8] Finite elastic eeformations and finite rotations of 3d continuum with independent rotation field, Revue européenne élém. finis, Volume 4 (1995), pp. 555-576
[9] An excursion into large rotations, Comput. Methods Appl. Mech. Engrg., Volume 32 (1982), pp. 85-155
[10] Rotation in computational solid mechanics, Arch. Comp. Mech., Volume 2 (1995), pp. 49-138
[11] Shell theory versus degeneration – a comparison in large rotation finite element analysis, Int. J. Numer. Methods Engrg., Volume 34 (1992), pp. 39-59
[12] Parametrization of finite rotations in computational dynamics, Revue européenne élém. finis, Volume 4 (1995), pp. 497-554
[13] Rotation angles, Comput. Methods Appl. Mech. Engrg., Volume 105 (1993), pp. 111-124
[14] Computational aspects of vector-like parameterization of three-dimensional finite rotations, Int. J. Numer. Methods Engrg., Volume 38 (1995), pp. 3653-3673
[15] On the choice of finite rotation parameters, Comput. Methods Appl. Mech. Engrg., Volume 149 (1997), pp. 49-71
[16] Three-dimensional finite strain model. Part II: Computational aspects, Comput. Methods Appl. Mech. Engrg., Volume 38 (1986), pp. 79-118
[17] The (symmetric) Hessian for geometrically nonlinear models in solid mechanics: intrinsic definition and geometric interpretation, Comput. Methods Appl. Mech. Engrg., Volume 96 (1992), pp. 183-200
[18] Nonlinear dynamics of flexible multibody systems, Comp. Structures, Volume 81 (2003), pp. 1113-1132
[19] Optimal control of structures undergoing finite rotations, Int. J. Numer. Methods Engrg., Volume 58 (2003) (in press)
[20] Shape optimization of elastic structural systems undergoing large rotations: Simultaneous solution procedure, Int. J. Comput. Model. Engrg. Sci., Volume 5 (2003) (in press)
[21] Mathematical Foundations of Elasticity, Dover, New York, 1994
[22] Cours de mécanique de l'École Polytechnique, Tome 1, Ellipses, Paris, 1986
[23] Theoretical Elasticity, Dover, New York, 1992
[24] The Non-Linear Field Theories, Springer, Berlin, 1965
[25] Mathematical Elasticity, North-Holland, 1988
[26] The Finite Element Method. Vols. I–III, Butterworth–Heinemann, Oxford, 2000
[27] Modélisation et calcul des grands déplacements de tuyaux élastiques en flexion–torsion, J. Méc., Volume 7 (1988), pp. 379-408
[28] Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation, Proc. Roy. Soc. London Ser. A, Volume 455 (1999), pp. 1125-1147
[29] On the role of geometrically exact and second order theories in buckling and post-buckling analysis of three-dimensional beam structures, Comp. Structures, Volume 61 (1996), pp. 1101-1114
[30] Nonlinear dynamics of three-dimensional rods: Exact energy and momentum conserving algorithm, Int. J. Numer. Methods Engrg., Volume 38 (1995), pp. 1431-1473
[31] On the role of frame-invariance of structural mechanics models at finite rotations, Comput. Methods Appl. Mech. Engrg., Volume 191 (2002), pp. 5159-5176
[32] The dynamics of flexible bodies, Int. J. Engrg. Sci., Volume 14 (1976), pp. 895-913
[33] Dynamics: Theory and Applications, McGraw-Hill, New York, 1985
[34] Energy conserving/decaying implicit time-stepping scheme for nonlinear dynamics of 3d beams undergoing finite rotations, Comput. Methods Appl. Mech. Engrg., Volume 191 (2002), pp. 4241-4258
[35] Microscale and mesoscale discrete models for dynamic fracture of structures built of brittle materials, Comp. Structures, Volume 81 (2003), pp. 1255-1265
[36] Introduction à l'analyse numérique matricielle et à l'optimisation, Masson, 1990
[37] Numerical Analysis of Parameterized Nonlinear Equations, Wiley, London, 1986
[38] Quadratically convergent direct calculation of critical points for 3d structures undergoing finite rotations, Comput. Methods Appl. Mech. Engrg., Volume 189 (2000), pp. 107-120
[39] An Exploration of Chaos, North-Holland, Amsterdam, 1994
[40] Solving Ordinary Differential Equations: Stiff and Differential-Algebraic Problems, Springer, Berlin, 1991
[41] Parameter Sensitivity in Nonlinear Mechanics; Theory and Finite Element Computations, Wiley, 1997
[42] A finite strain rod model and its design sensitivity, Mech. Struct. Mach., Volume 20 (1992), pp. 413-432
[43] Nonlinear shell problem formulation accouning for through-the-thickness stretching and its finite element implementation, Comput. Stuctures, Volume 80 (2002), pp. 699-717
[44] Dynamics and time-integration for elastic shells undergoing finite rotations, Comput. Stuctures, Volume 81 (2003), pp. 1193-1210
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