Refined Analysis of Torsion and In-plane Shear of Honeycomb Sandwich Structures

Abstract

Multiple-Pass Homogenization (MPH) technique is used to derive formulas for equivalent torsional and in-plane shear stiffness properties of sandwich plates with periodic core structures. In the first pass of the MPH, a discrete core structure is homogenized in a principal axis resulting in piecewise constant material properties, based on which the second pass can be analytically processed with respect to macroscopic torsion and in-plane shear modes. Two equivalent shear stiffness properties of periodic core structures, G ^* _cxy and G ^* _cxy, corresponding to torsion and in-plane shear, respectively, are conceptually and analytically distinguished from each other. By using the Saint-Venant’s semi-inverse method and periodic boundary conditions, analytical solutions of the equivalent shear stiffness are explicitly obtained in the form of Fourier series, which consist of a Voigt-type upper bound term and a correction term. Effects of thickness ratio and core transverse shear stiffness on the two equivalent shear stiffness properties are assessed and discussed. The approximation scheme proposed by this study improves modeling of sandwich structures as orthotropic plates, which is expected to be useful in the practical design and optimization of sandwich structures.

Keywords

torsional stiffness equivalent in-plane shear stiffness sandwich plates sandwich structures honeycomb homogenization Multi-Pass Homogenization (MPH)

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References

Muskhelishvili, N.I. (1953). Some Basic Problems of The Mathematical Theory of Elasticity, P. Noordhoff Ltd .

Lekhnitskii, S.G. (1963). Theory of Elasticity of an Anisotropic Body, Holden-Day Inc., San Francisco, CA .

Seide, P. (1956). On the Torsion of Rectangular Sandwich Plates , Journal of Applied Mechanics, 3(2): 191-194 .

Cheng, S. (1961). A Formula for Torsional Stiffness of Rectangular Sandwich Plates , Journal of Applied Mechanics, 83 .

Cheng, S. (1968). Elasticity Solution of Torsion of Sandwich Plates , Journal of the Engineering Mechanics Division, 94(EM2): 605-620 .

Whitney, J.M. (1991). Stress Analysis of Laminated, Anisotropic Plates Subjected to Torsional Loading , In: Proc. 32nd AIAA/ASME/ASCE/AHS/ASC/Structures, Structural Dynamics, and Materials Conf., Part 2, Structures and Design, AIAA Paper No. 91-0956, AIAA, Washington, DC, pp. 956-962 .

Whitney, J.M. (1993). Analysis of Anisotropic Laminated Plates Subjected to Torsional Loading , Composites Engineering, 3(6): 567-582 .

Whitney, J.M. and Kurtz, R.D. (1993). Analysis of Orthotropic Laminated Plates Subjected to Torsional Loading , Composites Engineering, 3(1): 83-97 .

Vinson, J.R. (1999). The Behavior of Sandwich Structures of Isotropic and Composite Materials, Technomic Publishing Co. Inc., Lancaster, PA .

10.

Gibson, L.J. and Ashby, M.F. (1988). Cellular Solids: Structure and Properties, Pergamon, Oxford .

11.

Shi, G. and Tong, P. (1995). Equivalent Transverse Shear Stiffness of Honeycomb Cores , Int. J. Solids Structures, 32(10): 1383-1393 .

12.

Shi, G. and Tong, P. (1995). The Derivation of Equivalent Constitutive Equations of Honeycomb Structures by a Two Scale Method , Computational Mechanics, 15: 395-407 .

13.

Xu, X.F. , Qiao, P.Z. and Davalos, J.F. (2001). On the Transverse Shear Stiffness of Composite Honeycomb Core with General Configuration , Journal of Engineering Mechanics, 127(11): 1144-1151 .

14.

Xu, X.F. and Qiao, P.Z. (2002). Homogenized Elastic Properties of Honeycomb Sandwiches with the Skin Effect , Int. J. Solids Structures, 39(8): 2153-2188 .

15.

Lewinski, T. (1991). Effective Models of Composite Periodic Plates - I. Asymptotic Solution. II. Simplifications Due to Symmetries. III. Two-Dimensional Approaches , Int. J. Solids Structures, 27: 1155-1203 .

16.

Davalos, J.F. , Qiao, P.Z. , Xu, X.F. , Robinson, J. and Barth, K.E. (2001). Modeling and Characterization of Fiber-reinforced Plastic Honeycomb Sandwich Panels for Highway Bridge Applications , Journal of Composite Structures, 52(3-4): 441-452 .

17.

Qiao, P.Z. and Wang, J.L. (2005). On the Mechanics of Composite Sinusoidal Honeycomb Cores , Journal of Aerospace Engineering, 18(1): 1-10 .

18.

Masters, I.G. and Evans, K.E. (1996). Models for the Elastic Deformation of Honeycombs , Composite Structures, 35: 403-422 .

19.

Xu, X.F. (2001). On the Elastic Homogenization of Honeycomb Sandwich Structures, Master of Science Thesis, Department of Civil Engineering, The University of Akron, Akron, Ohio.