Mathematical modelling of rods

Trabucho, L.; Viaño, J. M.

doi:10.1016/s1570-8659(96)80006-8

Cited by 165 publications

(246 citation statements)

References 74 publications

Supporting

Mentioning

222

Contrasting

Unclassified

Order By: Relevance

“…Particularly, periodic lattices have been studied through various approaches such as transfer matrices, variational calculus [Kerr and Accorsi 1985], and finite difference operators [Renton 1984]; see also the reviews [Noor 1988;Mead 1996]. Asymptotic homogenization methods [Sánchez-Palencia 1980] have been developed for homogeneous and periodic beams [Trabucho and Viaño 1996;Buannic and Cartraud 2001a;2001b], for periodic discrete structures [Bakhvalov and Panasenko 1989;Caillerie et al 1989], and in parallel with the homogenization of periodic media with multiple parameters and scale changes [Cioranescu and Saint Jean Paulin 1999]. Amongst the applications of homogenization of periodic discrete media (HPDM) we mention the papers [Tollenaere 1994;Moreau and Caillerie 1998;Boutin and Hans 2003], dealing respectively with the statics, buckling and dynamics of trusses; [Pradel and Sab 1998], on the constitutive laws of foams; and [Le Corre et al 2004], involving fluid mechanics.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of discrete framed structures: a unified homogenized description

Hans

Boutin

2008

JOMMS

View full text Add to dashboard Cite

The dynamic behavior of discrete periodic one-dimensional structures is approached by considering transverse vibrations of structures made of repeated unbraced frames. Assuming the frame size is small compared to the modal wavelength, equivalent macroscopic beam descriptions are obtained by the homogenization method of periodic discrete media. The macroscopic parameters are expressed as functions of the mechanical and geometrical properties of the frame elements.Depending on the order of magnitude (relative to the scale ratio) of the shear force, the global bending and the inner bending, four families of beams are shown to be possible. A generic beam governed by a differential equation of the sixth degree is shown to encompass all the other types.Simple criteria are established to identify the relevant model for real structures. A comparison of these theoretical results with numerical modeling is satisfactory even in the case of weak scale separation. In fact, an investigation of the higher orders terms shows that zero order descriptions are valid up to the second order. Lastly, analogies with micromorphic media are discussed.

show abstract

Section: Introductionmentioning

confidence: 99%

Dynamics of discrete framed structures: a unified homogenized description

Hans

Boutin

2008

JOMMS

View full text Add to dashboard Cite

show abstract

“…These justifications, which start from the three-dimensional theory, are made by using either formal asymptotic methods such as the method of asymptotic expansions or rigorous mathematical arguments such as À-convergence techniques. For further informations, the reader could refer to [35] for a broad review of the bibliography (up to 1996). Let us give a brief overview of those most important justifications.…”

Section: Introductionmentioning

confidence: 99%

Hierarchy of One-Dimensional Models in Nonlinear Elasticity

Marigo

Meunier

2006

J Elasticity

View full text Add to dashboard Cite

Abstract. By using formal asymptotic expansions, we build one-dimensional models for slender hyperelastic cylinders submitted to conservative loads. According to the order of magnitude of the applied loads, we obtain a hierarchy of models going from the linear theory of flexible bars to the nonlinear theory of extensible strings.Résumé. On construit, à l'aide de développements asymptotiques formels, des modèles unidimensionnels de cylindres hyperélastiques élancés soumis à des forces conservatives. Suivant l'ordre de grandeur des forces appliquées, on obtient une hiérarchie de modèles allant de la théorie des poutres flexibles jusqu'à la théorie des fils élastiques.Mathematics Subject Classifications (2000): 74K10, 74B05, 74G65, 74G10, 35A15, 35C20.

show abstract

“…For this reason, we determine the effective shear stiff ness coefficients by solving a free vibration problem. 1 The neces sity of considering free vibration problems for the determination of effective shear stiffness properties is also discussed in details in [20] Section 6, and in [21, pp. 34 38].…”

Section: Deformation Of Non Homogeneous Three Dimensional Rodsmentioning

confidence: 99%