A Local Model for Bending of Weak Core Sandwich Plates

Abstract

A bending theory is developed for a three-layer sandwich plate consisting of a weak core and two unequal face sheets. In the model, the core and face sheets are modeled as separate homogeneous plates with an assumed stress field, which satisfies equilibrium point-by-point. Local bending, including shear deformation, of the face sheets is taken into account. Although the usual assumption of negligible in-plane stresses in conjunction with a weak core is adopted, the effects of interlaminar core shear and normal stresses, along with transverse core flexibility, are included in the analysis. The corresponding displacement field consists of a combination of assumed and weighted displacements. Field equations are developed from Reissner’s energy theorem, and appropriate continuity conditions between the core and face sheets are enforced. The theory is applied to a rectangular plate subjected to a distributed load and to an end-loaded cantilever plate under cylindrical bending.

Keywords

sandwich plate interlaminar stresses bending concentrated load free-edge effects

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References

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

2. Librescu, L. , “Substantiation of the Theory of Anisotropic, Elastic, and Sandwich Flat Plates,” Chapter V in Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-type Structures, Noordhoff International Publishing, Co., Leyden, The Netherlands, 1975, pp. 493-513.

3. Frostig, Y. , Baruch, M. , Vilnay, O. and Sheinman, I. , “A Higher Order Theory for the Bending of Sandwich Beams with a Flexible Core,” Journal of the Engineering Mechanics Division, ASCE, Vol. 118, No. 5, 1992, pp. 1026-1043.

4. Frostig, Y. , “On Stress Concentration in the Bending of Sandwich Beams with Transversely Flexible Core,” Composite Structures, Vol. 24, No. 2, 1993, pp. 161-169.

5. Frostig, Y. and Shenhar, Y. , “High-Order Bending of Sandwich Beams with Transversely Flexible Core and Unsymmetrical Laminated Composite Skin,” Composites Engineering, Vol. 5, No. 4, 1995, pp. 405-414.

6. Frostig, Y. and Baruch, M. , “Localized Load Effects in High-Order Bending of Sandwich Panels with Flexible Core,” Journal of the Engineering Mechanics Division, ASCE, Vol. 122, No. 5, 1996, pp. 1069-1076.

7. Thomsen, O. T. , “High-Order Plate Formulation for the Modeling of Multiple Layer Sandwich Structures,” Proceedings of the American Society for Composites, Fourteenth Technical Conference, Edited by J. M. Whitney , Technomic Publishing Co., Lancaster, PA, 1999, pp. 414-423.

8. Pagano, N. J. , “Stress Fields in Composite Laminates,” International Journal of Solids and Structures, Vol. 14, 1978, pp. 385-400.

9. Reissner, E. , “On a Variational Theorem in Elasticity,” Journal of Mathematics and Physics, Vol. 29, 1950, pp. 90-95.

10.

10. Pagano, N. J. , “Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates,” Journal of Composite Materials, Vol. 4, January 1970, pp. 20-34.

11.

11. Pagano, N. J. and Soni, S. R. , “Global-Local Laminate Variational Model,” International Journal of Solids and Structures, Vol. 19, No. 3, 1983, pp. 207-228.