Homogenization of cellular sandwich panels

Arthur Lebée; Karam Sab

doi:10.1016/j.crme.2012.02.014

Homogenization of cellular sandwich panels

Arthur Lebée ¹ ; Karam Sab ¹

¹ Université Paris-Est, laboratoire Navier (École des Ponts ParisTech, IFSTTAR, CNRS), École des Ponts ParisTech, 6 et 8, avenue Blaise-Pascal, 77455 Marne-la-Vallée cedex 2, France

Comptes Rendus. Mécanique, Volume 340 (2012) no. 4-5, pp. 320-337.

Résumé

The Bending-Gradient plate theory originally presented in Lebée and Sab (International Journal of Solids and Structures 48 (2011) 2878–2888) is applied to cellular sandwich panels. This theory is the extension of the Reissner–Mindlin theory to heterogeneous plates. Its application clarifies common assumptions made in sandwich theory. It also enables to define a direct homogenization scheme for deriving the shear forces stiffness of sandwich panels. Finally, the conventional bounds used for estimating sandwich panels stiffnesses are justified.

Publié le : 2012-03-29

DOI : 10.1016/j.crme.2012.02.014

Mots clés : Plate theory, Sandwich panels, Homogenization, Periodic plates, Higher-order models

Affiliations des auteurs :

Arthur Lebée ¹ ; Karam Sab ¹

¹ Université Paris-Est, laboratoire Navier (École des Ponts ParisTech, IFSTTAR, CNRS), École des Ponts ParisTech, 6 et 8, avenue Blaise-Pascal, 77455 Marne-la-Vallée cedex 2, France

@article{CRMECA_2012__340_4-5_320_0,
     author = {Arthur Leb\'ee and Karam Sab},
     title = {Homogenization of cellular sandwich panels},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {320--337},
     publisher = {Elsevier},
     volume = {340},
     number = {4-5},
     year = {2012},
     doi = {10.1016/j.crme.2012.02.014},
     language = {en},
}

TY  - JOUR
AU  - Arthur Lebée
AU  - Karam Sab
TI  - Homogenization of cellular sandwich panels
JO  - Comptes Rendus. Mécanique
PY  - 2012
SP  - 320
EP  - 337
VL  - 340
IS  - 4-5
PB  - Elsevier
DO  - 10.1016/j.crme.2012.02.014
LA  - en
ID  - CRMECA_2012__340_4-5_320_0
ER  -

%0 Journal Article
%A Arthur Lebée
%A Karam Sab
%T Homogenization of cellular sandwich panels
%J Comptes Rendus. Mécanique
%D 2012
%P 320-337
%V 340
%N 4-5
%I Elsevier
%R 10.1016/j.crme.2012.02.014
%G en
%F CRMECA_2012__340_4-5_320_0

Arthur Lebée; Karam Sab. Homogenization of cellular sandwich panels. Comptes Rendus. Mécanique, Volume 340 (2012) no. 4-5, pp. 320-337. doi : 10.1016/j.crme.2012.02.014. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.02.014/

Bibliographie
Cité par

[1] V.S. Deshpande; N.A. Fleck Collapse of truss core sandwich beams in 3-point bending, International Journal of Solids and Structures, Volume 38 (2001), pp. 6275-6305

[2] K. Miura Zeta-core sandwich – its concept and realization, ISAS Report, Volume 37 (1972), pp. 137-164

[3] H. Allen Analysis and Design of Structural Sandwich Panels, Pergamon Press, 1969

[4] A.K. Noor; W.S. Burton; C.W. Bert Computational models for sandwich panels and shells, Applied Mechanics Reviews, Volume 49 (1996), pp. 155-199

[5] J. Hohe; W. Becker Effective stress-strain relations for two-dimensional cellular sandwich cores: Homogenization, material models, and properties, Applied Mechanics Reviews, Volume 55 (2002), pp. 61-87

[6] E. Reissner The effect of transverse shear deformation on the bending of elastic plates, Journal of Applied Mechanics, Volume 12 (1945), pp. 68-77

[7] R. Mindlin Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, Journal of Applied Mechanics, Volume 18 (1951), pp. 31-38

[8] A. Lebée; K. Sab A bending-gradient model for thick plates. Part I: Theory, International Journal of Solids and Structures, Volume 48 (2011), pp. 2878-2888

[9] A. Lebée, Thick periodic plates homogenization, application to sandwich panels including chevron folded core, Ph.D. thesis, Université Paris-Est, 2010.

[10] E. Reissner On bending of elastic plates, Quarterly of Applied Mathematics, Volume 5 (1947), pp. 55-68

[11] E. Reissner, Small bending and stretching of sandwich-type shells, Tech. Rep. 1832, NACA, 1949.

[12] Hexcel, Honeycomb Sandwich Design Technology, Hexcel, 2000.

[13] S. Kelsey; R.A. Gellatly; B.W. Clark The shear modulus of foil honeycomb cores: A theoretical and experimental investigation on cores used in sandwich construction, Aircraft Engineering and Aerospace Technology, Volume 30 (1958), pp. 294-302

[14] J.N. Reddy On refined computational models of composite laminates, International Journal for Numerical Methods in Engineering, Volume 27 (1989), pp. 361-382

[15] H. Altenbach Theories for laminated and sandwich plates. A review, Mechanics of Composite Materials, Volume 34 (1998), pp. 243-252

[16] A.K. Noor; M. Malik An assessment of five modeling approaches for thermo-mechanical stress analysis of laminated composite panels, Computational Mechanics, Volume 25 (2000), pp. 43-58

[17] E. Carrera Theories and finite elements for multilayered, anisotropic, composite plates and shells, Archives of Computational Methods in Engineering, Volume 9 (2002), pp. 87-140

[18] C. Libove, S. Batdorf, General small-deflection theory for flat sandwich plates, Tech. Rep, NACA, Washington, DC, 1948.

[19] J.R. Vinson Governing equations for plates and panels of sandwich construction, Solid Mechanics and Its Applications, vol. 120, Springer, Netherlands, 2005, pp. 295-303

[20] V. Birman; C.W. Bert On the choice of shear correction factor in sandwich structures, Journal of Sandwich Structures and Materials, Volume 4 (2002), pp. 83-95

[21] G. Shi; P. Tong The derivation of equivalent constitutive equations of honeycomb structures by a two scale method, Computational Mechanics, Volume 15 (1995), pp. 395-407

[22] X.F. Xu; P. Qiao; J.F. Davalos Transverse shear stiffness of composite honeycomb core with general configuration, Journal of Engineering Mechanics, Volume 127 (2001), pp. 1144-1151

[23] J. Hohe; W. Becker A mechanical model for two-dimensional cellular sandwich cores with general geometry, Computational Materials Science, Volume 19 (2000), pp. 108-115

[24] J. Hohe; W. Becker An energetic homogenisation procedure for the elastic properties of general cellular sandwich cores, Composites Part B: Engineering, Volume 32 (2001), pp. 185-197

[25] J. Penzien; T. Didriksson Effective shear modulus of honeycomb cellular structure, AIAA Journal, Volume 2 (1964), pp. 531-535

[26] M. Grediac A finite-element study of the transverse-shear in honeycomb-cores, International Journal of Solids and Structures, Volume 30 (1993), pp. 1777-1788

[27] W. Becker The in-plane stiffnesses of a honeycomb core including the thickness effect, Archive of Applied Mechanics, Volume 68 (1998), pp. 334-341

[28] A. Chen; J.F. Davalos A solution including skin effect for stiffness and stress field of sandwich honeycomb core, International Journal of Solids and Structures, Volume 42 (2005), pp. 2711-2739

[29] A. Chen; J.F. Davalos Transverse shear including skin effect for composite sandwich with honeycomb sinusoidal core, Journal of Engineering Mechanics, Volume 133 (2007), pp. 247-256

[30] G. Shi; P. Tong Equivalent transverse shear stiffness of honeycomb cores, International Journal of Solids and Structures, Volume 32 (1995), pp. 1383-1393

[31] T.M. Nordstrand; L.A. Carlsson Evaluation of transverse shear stiffness of structural core sandwich plates, Composite Structures, Volume 37 (1997), pp. 145-153

[32] A. Lebée; K. Sab Transverse shear stiffness of a chevron folded core used in sandwich construction, International Journal of Solids and Structures, Volume 47 (2010), pp. 2620-2629

[33] A. Lebée; K. Sab Homogenization of thick periodic plates: application of the bending-gradient plate theory to folded core sandwich panel, International Journal of Solids and Structures (2012) | DOI

[34] N. Buannic; P. Cartraud; T. Quesnel Homogenization of corrugated core sandwich panels, Composite Structures, Volume 59 (2003), pp. 299-312

[35] J. Hohe A direct homogenisation approach for determination of the stiffness matrix for microheterogeneous plates with application to sandwich panels, Composites Part B: Engineering, Volume 34 (2003), pp. 615-626

[36] A. Cecchi; K. Sab A homogenized Reissner–Mindlin model for orthotropic periodic plates: Application to brickwork panels, International Journal of Solids and Structures, Volume 44 (2007), pp. 6055-6079

[37] J. Whitney Cylindrical bending of unsymmetrically laminated plates, Journal of Composite Materials, Volume 3 (1969), pp. 715-719

[38] A. Lebée; K. Sab A bending-gradient model for thick plates, Part II: Closed-form solutions for cylindrical bending of laminates, International Journal of Solids and Structures, Volume 48 (2011), pp. 2889-2901

[39] J.M. Whitney; A.W. Leissa Analysis of heterogeneous anisotropic plates, Journal of Applied Mechanics (1969), pp. 261-266

[40] D. Caillerie Thin elastic and periodic plates, Mathematical Methods in the Applied Sciences, Volume 6 (1984), pp. 159-191

[41] R.V. Kohn; M. Vogelius A new model for thin plates with rapidly varying thickness, International Journal of Solids and Structures, Volume 20 (1984), pp. 333-350

[42] P.G. Ciarlet; P. Destuynder Justification of the 2-dimensional linear plate model, Journal de Mecanique, Volume 18 (1979), pp. 315-344

[43] A.G. Kolpakov; I.G. Sheremet The stiffnesses of non-homogeneous plates, Journal of Applied Mathematics and Mechanics, Volume 63 (1999), pp. 633-640

[44] L.J. Gibson; M.F. Ashby Cellular Solids, Pergamon Press, 1988

[45] A. Lebée, K. Sab, Homogenization of a space frame as a thick plate: application of the bending-gradient theory to a beam lattice, submitted for publication.

[46] S. Vlachoutsis Shear correction factors for plates and shells, International Journal for Numerical Methods in Engineering, Volume 33 (1992), pp. 1537-1552

Cité par Sources :

Commentaires - Politique