Improved extended high order analysis of sandwich beams with a bilinear core shear behavior

Abstract

The response of a sandwich panel with bilinear constitutive behavior for shear stress of a core is presented based on a proposed improved extended high order sandwich panel theory. In this theory the face sheets are analyzed based on the first order shear deformation theory that is hitherto not applied in the conventional extended high order sandwich panel theory. Besides, the two-dimensional (2D) elasticity is used for the core. The field equations are derived using the Ritz-based solution which is suitable for any essential boundary condition. In each type of boundary conditions, the effects of plastic shear modulus of the core on transverse shear stress distribution within the core, transverse normal stresses at top and bottom face sheet–core interfaces, displacement components through the thickness of the core, as well as the force and moment resultants and transverse displacements in the face sheets are studied in detail. Also, all results based on the bilinear material assumption of the core are compared with the linear elastic ones. The results reveal that initial plastic regions are created at core edges. Furthermore, the absolute value of shear stresses in the plastic zones based on the bilinear analysis is lower than those obtained from linear elastic one for both types of the boundary conditions. It is seen that, unlike the case of the clamped edges, the plastic regions predicted by bilinear material behavior are much more extensive than ones resulted from elastic material behavior in the simply supported case. Finally, in the case of the linear elastic analysis, the results of the transverse deflections and shear stresses are compared with finite element simulation.

Keywords

Improved extended high order theory bilinear constitutive behavior shear plastic modulus Ritz method sandwich beam

Get full access to this article

View all access options for this article.

References

Gibson

Ashby

. Cellular solids: Structures and properties, Oxford: Pergamon Press, 1988.

Mines

RAW

Jones

. Approximate elastic-plastic analysis of the static and impact behavior of polymer composite sandwich beams. Composites 1995; 26: 803–814.

Lubin

. Handbook of composites, Cincinnati, NY: Van Nostrand Reinhold Company Regional Offices, 1981.

Klintworth

Stronge

. Elasto-plastic yield limits and deformation laws for transversely crushed honeycomb. Int J Mech Sci 1988; 30: 273–293.

Zhu

Mills

Knott

. Analysis of high strain compression of open-cell foams. J Mech Phys Solids 1997; 45: 1875–1904.

Sadighi

Jedari Salami

. An investigation on low-velocity impact response of elastomeric & crushable foams. Cent Eur J Eng 2012; 2: 627–637.

Mercado

Sikarskie

. On the response of a sandwich panel with a bilinear core. Mech Compos Mater Struct 1999; 6: 57–67.

Jaskula

Zielnica

. Large displacement stability analysis of elastic–plastic unsymmetrical sandwich cylindrical shells. Thin-Walled Struct 2011; 49: 611–617.

Zhang

Qin

Wang

. Compressive strengths and dynamic response of corrugated metal sandwich plates with unfilled and foam-filled sinusoidal plate cores. Acta Mech 2013; 224: 759–775.

10.

Liu

Chen

Yang

. Elastic-plastic dynamic response of fully backed sandwich plates under localized impulsive loading. Acta Mech Solida Sin 2010; 23: 324–335.

11.

Malver

. Introduction to the mechanics of a continuous medium, Englewood Cliffs, NJ: Prentice-Hall, 1969.

12.

. An elastic–plastic model on the dynamic response of composite sandwich beams subjected to mass impact. Compos Struct 2006; 72: 1–9.

13.

Hoo Fat

Chapagain

. Pressure pulse response of composite sandwich panels with plastic core damping. J Sandwich Struct Mater 2012; 14: 397–429.

14.

Chang

W-S

Krauthammer

Ventsel

. Elasto-plastic analysis of corrugated-core sandwich plates. Mech Adv Mater Struct 2006; 13: 151–160.

15.

Schwarts-Givli

Frostig

. High-order behavior of sandwich panels with a bilinear transversely flexible core. Compos Struct 2001; 53: 87–106.

16.

Frostig

Baruch

Vilnay

. High-order theory for sandwich-beam behavior with transversely flexible core. J Eng Mech 1992; 118: 1026–1043.

17.

Vonach

Rammerstofer

. The effects of in-plane core stiffness on the wrinkling behavior of thick sandwiches. Acta Mech 2000; 141: 1–10.

18.

Carlsson LA and Kardomateas GA. Structural and failure mechanics of sandwich composites. New York: Springer, 2011.

19.

Phan

Frostig

Kardomateas

. Analysis of sandwich beams with a compliant core and with in-plane rigidity-extended high-order sandwich panel theory versus elasticity. J Appl Mech 2012; 79: 1–11.

20.

Phan

Kardomateas

Frostig

. Global buckling of sandwich beams based on the extended high-order theory. AIAA J 2012; 50: 1707–1716.

21.

Phan

Bailey

Kardomateas

. Wrinkling of sandwich wide panels/beams based on the extended high-order sandwich panel theory: formulation, comparison with elasticity and experiments. Arch Appl Mech 2012; 82: 1585–1599.

22.

Reddy JN. Mechanics of laminated composite plates and shells: Theory and analysis. New York: CRC Press, 2003.

23.

Abrate S. Impact on composite structures. New York: Cambridge University Press, 1998.

24.

Kim

Swanson

. Design of sandwich structures for concentrated loading. Comp Struct 2001; 52: 365–373.

25.

Alderliesten

Campoli

Benedictus

. Modelling cyclic shear deformation of fibre/epoxy layers in fibre metal laminates. Comp Sci Technol 2007; 67: 2545–2555.

26.

Abaqus analysis user’s manual, Elements for linear analysis of bending problems, ABAQUS ver. 6.10.