A higher-order zig-zag theory has been developed for laminated composite plates with multiple delaminations. By imposing top and bottom surface transverse shear stress-free conditions and interface continuity conditions of transverse shear stresses including delaminated interfaces, the displacement field with minimal degree-of-freedoms are obtained. This displacement field can systematically handle the number, shape, size, and locations of delaminations. Through the dynamic version of variational approach, the dynamic equilibrium equations and variationally consistent boundary conditions are obtained. The delaminated beam finite element is implemented to evaluate the performance of the newly developed theory. Linear buckling and natural frequency analysis demonstrate the accuracy and efficiency of the present theory. The present higher-order zig-zag theory should work as an efficient tool to analyze the static and dynamic behavior of the composite plates with multiple delaminations.

1.
Lo
,
K. H.
,
Christensen
,
R. M.
, and
Wu
,
E. M.
,
1977
, “
A Higher-Order Theory of Plate Deformation, Part 2: Laminated Plates
,”
ASME J. Appl. Mech.
,
44
, pp.
669
676
.
2.
Reddy
,
J. N.
,
1987
, “
A Generalization of Two-Dimensional Theories of Laminated Plates
,”
Commun. Appl. Numer. Methods
,
3
, pp.
173
180
.
3.
Di Sciuva
,
M.
,
1986
, “
Bending, Vibration and Buckling of Simply Supported Thick Multilayered Orthotropic Plates: An Evaluation of a New Displacement Model
,”
J. Sound Vib.
,
105
, pp.
425
442
.
4.
Noor
,
A. K.
, and
Burton
,
W. S.
,
1989
, “
Assessment of Shear Deformation Theories for Multilayered Composite Plates
,”
Appl. Mech. Rev.
,
42
, pp.
1
13
.
5.
Kapania
,
R. K.
, and
Raciti
,
S.
,
1989
, “
Recent Advanced in Analysis of Laminated Beams and Plates
,”
AIAA J.
,
27
, pp.
923
946
.
6.
Reddy
,
J. N.
, and
Robbins
,
D. H.
Jr.,
1994
, “
Theories and Computational Models for Composite Laminates
,”
Appl. Mech. Rev.
,
47
, pp.
147
169
.
7.
Simitses, G. J., 1995, “Delamination Buckling of Flat Laminates,” Buckling and Postbuckling of Composite Plates, G. J. Turvey and I. H. Marshall, eds., Chapman & Hall, London, pp. 299–328.
8.
Wang
,
J. T. S.
,
Liu
,
Y. Y.
, and
Gibby
,
J. A.
,
1982
, “
Vibrations of Split Beams
,”
J. Sound Vib.
,
84
, pp.
491
502
.
9.
Wang, J. T. S., and Lin, C. C., 1995, “Vibration of Beam-Plates Having Multiple Delaminations,” Proceedings of the AIAA/ASME/ASCE/AHS/ASC 36th Structures, Structural Dynamics and Materials Conference, New Orleans, LA, AIAA, Reston, VA, pp. 3126–3133.
10.
Shen
,
M.-H. H.
, and
Grady
,
J. E.
,
1992
, “
Free Vibration of Delaminated Beams
,”
AIAA J.
,
30
, pp.
1361
1370
.
11.
Gummadi, L. N. B., and Hanagud, S., 1995, “Vibration Characteristics of Beams With Multiple Delaminations,” Proceedings of the AIAA/ASME/ASCE/AHS/ASC 36th Structures, Structural Dynamics and Materials Conference, New Orleans, LA, AIAA, Reston, VA, pp. 140–150.
12.
Chattopadhyay
,
A.
,
Dragomir-Daescu
,
D.
, and
Gu
,
H.
,
1999
, “
Dynamics of Delaminated Smart Composite Cross-Ply Beams
,”
Smart Mater. Struct.
,
8
, pp.
92
99
.
13.
Seeley
,
C. E.
, and
Chattopadhyay
,
A.
,
1999
, “
Modeling of Adaptive Composites Including Debonding
,”
Int. J. Solids Struct.
,
36
, pp.
1823
1843
.
14.
Islam
,
A. S.
, and
Craig
,
K. C.
,
1994
, “
Damage Detection in Composite Structures Using Piezoelectric Materials
,”
Smart Mater. Struct.
,
3
, pp.
318
328
.
15.
Lee
,
J.
,
Gu¨rdal
,
Z.
, and
Griffin
,
O. H.
,
1993
, “
Layer-Wise Approach for the Bifurcation Problem in Laminated Composites With Delaminations
,”
AIAA J.
,
31
, pp.
331
338
.
16.
Cho
,
M.
, and
Kim
,
J.-S.
,
1997
, “
Bifurcation Buckling Analysis of Delaminated Composites Using Global-Local Approach
,”
AIAA J.
,
35
, pp.
1673
1676
.
17.
Cho, M., and Lee, S.-G., 1998, “Global/Local Analysis of Laminated Composites With Multiple Delaminations of Various Shapes,” Proceedings of the AIAA/ASME/ASCE/AHS/ASC 39th Structures, Structural Dynamics and Materials Conference, Long Beach, CA, AIAA, Reston, VA, pp. 76–86.
18.
Kim
,
J.-S.
, and
Cho
,
M.
,
1999
, “
Postbuckling of Delaminated Composites Under Compressive Loads Using Global-Local Approach
,”
AIAA J.
,
37
, pp.
774
777
.
19.
Cheng
,
Z-q.
,
Jemah
,
A. K.
, and
Williams
,
F. W.
,
1996
, “
Theory for Multilayered Anisotropic Plates With Weakened Interfaces
,”
ASME J. Appl. Mech.
,
63
, pp.
1019
1026
.
20.
Di Sciuva
,
M.
,
1997
, “
Geometrically Nonlinear Theory of Multilayered Plates With Interlayer Slips
,”
AIAA J.
,
35
, pp.
1753
1759
.
21.
Chattopadhyay
,
A.
, and
Gu
,
H.
,
1994
, “
New Higher Order Theory in Modeling Delamination Buckling of Composite Laminates
,”
AIAA J.
,
32
, pp.
1709
1716
.
22.
Cho
,
M.
, and
Parmerter
,
R. R.
,
1992
, “
An Efficient Higher-Order Plate Theory for Laminated Composites
,”
Composite Structures
,
20
, pp.
113
123
.
23.
Cho
,
M.
, and
Parmerter
,
R. R.
,
1993
, “
Efficient Higher Order Composite Plate Theory for General Lamination Configurations
,”
AIAA J.
,
31
, pp.
1299
1306
.
24.
Simitses
,
G. J.
,
Sallam
,
S.
, and
Yin
,
W. L.
,
1985
, “
Effect of Delamination of Axially Loaded Homogeneous Laminated Plates
,”
AIAA J.
,
23
, pp.
1437
1444
.
25.
Chen
,
H. P.
,
1991
, “
Shear Deformation Theory for Compressive Delamination Buckling and Growth
,”
AIAA J.
,
29
, pp.
813
819
.
26.
Gu
,
H.
, and
Chattopadhyay
,
A.
,
1998
, “
Elasticity Approach for Delamination Buckling of Composite Beam Plates
,”
AIAA J.
,
36
, pp.
2543
2551
.
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