Research Papers

Geometric Nonlinearity Effects in the Response of Sandwich Wide Panels

[+] Author and Article Information
Zhangxian Yuan

School of Aerospace Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0150

George A. Kardomateas

School of Aerospace Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0150

Yeoshua Frostig

Faculty of Civil and
Environmental Engineering,
Technion Israel Institute of Technology,
Haifa 32000, Israel

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 19, 2016; final manuscript received May 16, 2016; published online June 27, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(9), 091008 (Jun 27, 2016) (10 pages) Paper No: JAM-16-1194; doi: 10.1115/1.4033651 History: Received April 19, 2016; Revised May 16, 2016

In the literature, there are various simplifying assumptions adopted in the kinematic relations of the faces and the core when considering a geometrically nonlinear problem in sandwich structures. Most commonly, only one nonlinear term is included in the faces and the core nonlinearities are neglected. A critical assessment of these assumptions, as well as the effects of including the other nonlinear terms in the faces and the core, is the scope of this paper. The comprehensive investigation of all the nonlinear terms is accomplished by deriving and employing an advanced nonlinear high-order theory, namely, the recently developed “extended high-order sandwich panel theory” (EHSAPT). This theory, which was derived as a linear theory, is first formulated in this paper in its full nonlinear version for the simpler one-dimensional case of sandwich wide panels/beams. Large displacements and moderate rotations are taken into account in both faces and core. In addition, a nonlinear EHSAPT-based finite element (FE) is developed. A series of simplified models with various nonlinear terms included are derived accordingly to check the validity of each of these assumptions. Two sandwich panel configurations, one with a “soft” and one with a “hard” core, loaded in three-point bending, are analyzed. The geometric nonlinearity effects and the relative merits of the corresponding simplifications are analyzed with these two numerical examples. In addition to a relative comparison among all these different assumptions, the results are also compared to the corresponding ones from a commercial FE code.

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Carlsson, L. , and Kardomateas, G. A. , 2011, Structural and Failure Mechanics of Sandwich Composites, Springer, New York.
Pagano, N. , 1970, “ Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates,” J. Compos. Mater., 4(1), pp. 20–34.
Kardomateas, G. A. , 2011, “ Three Dimensional Elasticity Solution for Sandwich Beams/Wide Plates With Orthotropic Phases: The Negative Discriminant Case,” J. Sandwich Struct. Mater., 13(6), pp. 641–661. [CrossRef]
Plantema, F. J. , 1966, Sandwich Construction, Wiley, New York.
Allen, H. G. , 1969, Analysis and Design of Structural Sandwich Panels, Pergamon, Oxford, UK.
Frostig, Y. , Baruch, M. , Vilnay, O. , and Sheinman, I. , 1992, “ High-Order Theory for Sandwich-Beam Behavior With Transversely Flexible Core,” J. Eng. Mech., 118(5), pp. 1026–1043. [CrossRef]
Phan, C. N. , Frostig, Y. , and Kardomateas, G. A. , 2012, “ Analysis of Sandwich Panels With a Compliant Core and With In-Plane Rigidity-Extended High-Order Sandwich Panel Theory Versus Elasticity,” ASME J. Appl. Mech., 79(4), p. 041001. [CrossRef]
Sokolinsky, V. S. , Shen, H. , Vaikhanski, L. , and Nutt, S. R. , 2003, “ Experimental and Analytical Study of Nonlinear Bending Response of Sandwich Beams,” Compos. Struct., 60(2), pp. 219–229. [CrossRef]
Frostig, Y. , and Baruch, M. , 1993, “ High-Order Buckling Analysis of Sandwich Beams With Transversely Flexible Core,” J. Eng. Mech., 119(3), pp. 476–495. [CrossRef]
Sokolinsky, V. , and Frostig, Y. , 1999, “ Nonlinear Behavior of Sandwich Panels With a Transversely Flexible Core,” AIAA J., 37(11), pp. 1474–1482. [CrossRef]
Sokolinsky, V. , and Frostig, Y. , 2000, “ Branching Behavior in the Nonlinear Response of Sandwich Panels With a Transversely Flexible Core,” Int. J. Solids Struct., 37(40), pp. 5745–5772. [CrossRef]
Li, R. , and Kardomateas, G. A. , 2008, “ Nonlinear High-Order Core Theory for Sandwich Plates With Orthotropic Phases,” AIAA J., 46(11), pp. 2926–2934. [CrossRef]
Hohe, J. , and Librescu, L. , 2003, “ A Nonlinear Theory for Doubly Curved Anisotropic Sandwich Shells With Transversely Compressible Core,” Int. J. Solids Struct., 40(5), pp. 1059–1088. [CrossRef]
Frostig, Y. , Thomsen, O. T. , and Sheinman, I. , 2005, “ On the Non-Linear High-Order Theory of Unidirectional Sandwich Panels With a Transversely Flexible Core,” Int. J. Solids Struct., 42(5–6), pp. 1443–1463. [CrossRef]
Dariushi, S. , and Sadighi, M. , 2014, “ A New Nonlinear High Order Theory for Sandwich Beams: An Analytical and Experimental Investigation,” Compos. Struct., 108(0), pp. 779–788. [CrossRef]
Ganapathi, M. , Patel, B. P. , and Makhecha, D. P. , 2004, “ Nonlinear Dynamic Analysis of Thick Composite/Sandwich Laminates Using an Accurate Higher-Order Theory,” Composites, Part B, 35(4), pp. 345–355. [CrossRef]
Madhukar, S. , and Singha, M. K. , 2013, “ Geometrically Nonlinear Finite Element Analysis of Sandwich Plates Using Normal Deformation Theory,” Compos. Struct., 97(0), pp. 84–90. [CrossRef]
Hu, H. , Belouettar, S. , Potier-Ferry, M. , and Makradi, A. , 2009, “ A Novel Finite Element for Global and Local Buckling Analysis of Sandwich Beams,” Compos. Struct., 90(3), pp. 270–278. [CrossRef]
Elmalich, D. , and Rabinovitch, O. , 2012, “ A High-Order Finite Element for Dynamic Analysis of Soft-Core Sandwich Plates,” J. Sandwich Struct. Mater., 14(5), pp. 525–555.
Oskooei, S. , and Hansen, J. S. , 2000, “ Higher-Order Finite Element for Sandwich Plates,” AIAA J., 38(3), pp. 525–533. [CrossRef]
Yuan, Z. , Kardomateas, G. A. , and Frostig, Y. , 2015, “ Finite Element Formulation Based on the Extended High-Order Sandwich Panel Theory,” AIAA J., 52(10), pp. 3006–3015. [CrossRef]
Crisfield, M. A. , 1981, “ A Fast Incremental/Iterative Solution Procedure That Handles Snap-Through,” Comput. Struct., 13(1–3), pp. 55–62. [CrossRef]
Crisfield, M. A. , 1983, “ An Arc-Length Method Including Line Searches and Accelerations,” Int. J. Numer. Methods Eng., 19(9), pp. 1269–1289. [CrossRef]


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Fig. 1

Definition of the geometry and coordinate system for the sandwich panel

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Fig. 2

Sketch of the EHSAPT-based FE model (two-node element)

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Fig. 5

Displacement profile in faces and core at P=1300N: (a) axial displacement and (b) transverse displacement

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Fig. 8

Resultant axial force versus applied load

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Fig. 6

Strain and stress distribution in the core at x=0.5a : (a) axial strain, (b) transverse normal strain, (c) axial stress, and (d) transverse normal stress

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Fig. 7

Strain and stress distribution in the core at x=0.4a : (a) axial strain, (b) transverse normal strain, (c) axial stress, (d) transverse normal stress, and (e) shear stress

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Fig. 9

Load versus midspan displacement of sandwich panel with moderate core

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Fig. 4

Load versus midspan displacement of sandwich panel with soft core



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