This paper deals with buckling and vibration analysis of initially stressed damped composite sandwich plates using assumed strain finite elements. A family of plate bending elements containing nine degrees of freedom per node are developed based on a refined higher-order shear deformation theory. The higher-order theory contains in-plane displacements that are expanded to include the higher-order terms in the Taylor series expansion as a result of which there is no need for shear correction factors. The popular assumed strain concept is used to ensure that the developed four- and nine-node elements pass the patch test and show no signs of shear locking and spurious zero energy modes in the present finite element formulations. Parametric studies are carried out to study the behavior of length to thickness ratios, boundary conditions, fiber orientations on vibration, and buckling of damped composite sandwich plates.
Chandra, R. , Singh, S.P. and Gupta, K. (1999). Damping Studies in Fiber-reinforced Composites - A Review , Composite Structures, 46(1): 41-51 .
2.
Finegan, I.C. and Gibson, R.F. (1999). Recent Research on Enhancement of Damping in Polymer Composites , Composite Structures, 44(2-3): 89-98 .
3.
Chung, D.D.L. (2003). Structural Composite Materials Tailored for Damping , Journal of Alloys and Compounds, 355(1-2): 216-223 .
4.
Chandra, R. , Singh, S.P. and Gupta, K. (2003). Experimental Evaluation of Damping of Fiber-reinforced Composites , Journal of Composites Technology and Research, 25(2): 96-107 .
5.
Chandra, R. , Singh, S.P. and Gupta, K. (2002). Micromechanical Damping Models for Fiber-reinforced Composites: A Comparative Study , Composites Part A - Applied Science and Manufacturing, 33(6): 787-796 .
6.
Meunier, M. and Shenoi, R.A. (2001). Dynamic Analysis of Composite Sandwich Plates with Damping Modelled using High-order Shear Deformation Theory , Composite Structures, 54(2-3): 243-254 .
7.
Noor, A.K. (1975). Stability of Multilayered Composite Plates , Fibre Science and Technology, 8(2): 81-89 .
8.
Noor, A.K. (1973). Free Vibrations of Multilayered Composite Plates , AIAA Journal, 11: 1038-1039 .
9.
Noor, A.K. , Peters, J.M. and Burton, W.S. (1994). 3-Dimensional Solutions for Initially Stressed Structural Sandwiches , J. Engg. Mech., ASCE, 120(2): 284-303 .
10.
Noor, A.K. , Burton, W.S. and Bert, C.W. (1996). Computational Models for Sandwich Panels and Shells, Applied Mechanics Reviews , Transactions of ASME, 49(3): 155-199 .
11.
Mallikarjuna and Kant, T. (1993). A Critical Review and Some Results of Recently Developed Refined Theories of Fiber Reinforced Laminated Composites and Sandwiches , Composite Structures, 23(4): 293-312 .
12.
Kant, T. and Swaminathan, K. (2001). Analytical Solutions for Free Vibration of Laminated Composite and Sandwich Plates based on a Higher Order Refined Theory , Composite Structures, 53(1): 73-85 .
13.
Kant, T. and Swaminathan, K. (2001). Free Vibration of Isotropic, Orthotropic and Multilayer Plates based on Higher Order Refined Theories , Journal of Sound and Vibration, 241(2): 319-327 .
14.
Kant, T. and Swaminathan, K. (2000). Analytical Solutions using a Higher Order Refined Theory for the Stability Analysis of Laminated Composite and Sandwich Plates , Structural Engineering and Mechanics, 10(4): 337-357 .
15.
Reddy, J.N. and Robbins, D.H., Jr. (1994). Theories and Computational Models for Composite Laminates, Applied Mechanics Reviews , Transactions of The American Society of Mechanical Engineers, 47: 147-169 .
16.
Vlachoutsis, S. (1992). Shear Correction Factors for Plates and Shells . International Journal for Numerical Methods in Engineering, 33(7): 1537-1552 .
17.
Rikards, R. , Chate, A. and Korjakin, A. (1995). Vibration and Damping Analysis of Laminated Composite Plates by the Finite Element Method , Engineering Computations, 12: 61-74 .
18.
Carrera, E. (2003). Theories and Finite Elements for Multilayered Plates and Shells: A Unified Compact Formulation with Numerical Assessment and Benchmarking , Archives of Computational Methods in Engineering, 10: 215-296 .
19.
Reddy, J.N. (1984). A Simple Higher Order Theory for Laminated Composite Plates , Journal of Applied Mechanics, Trans. ASME, 51: 745-752 .
20.
Murakami, H. (1986). Laminated Composite Plate Theory with Improved In-plane Responses , Journal of Applied Mechanics, Trans. ASME, 53: 661-666 .
21.
Cho, M. and Parmerter, R.R. (1993). Efficient Higher Order Composite Plate Theory for General Lamination Configurations , AIAA Journal, 31(7): 1299-1306 .
22.
Yang, H.T.Y. , Saigal, S. , Masud, A. and Kapania, R.K. (2000). A Survey of Recent Shell Finite Elements , International Journal for Numerical Methods in Engineering, 47: 101-127 .
23.
Ganapathi, M. , Polit, O. and Touratier, M. (1996). A Co Eight-node Membrane-shear-bending Element for Geometrically Non-linear (Static-dynamic) Analysis of Laminates , International Journal for Numerical Methods in Engineering, 39: 3453-3474 .
24.
Babu, C.S. and Kant, T. (1999). Two Shear Deformable Finite Element Models for Buckling Analysis for Skew Fibre-reinforced Composite and Sandwich Panels , Composite Structures, 46: 115-124 .
25.
Topdar, P. , Sheikh, A.H. and Dhang, N. (2003). Finite Element Analysis of Composite and Sandwich Plates using a Continuous Inter-laminar Shear Stress Model , Journal of Sandwich Structures and Materials, 5: 207-231 .
26.
Mackerle, J. (2002). Finite Element Analysis of Sandwich Structures: A Bibliography (1980-2001) , Engineering Computations, 19: 206-245 .
27.
Bathe, K.J. , Iosilevich, A. and Chapelle, D. (2000). An Evaluation of the MITC Shell Elements , Computers and Structures, 75(1): 1-30 .
28.
Lee, P.S. and Bathe, K.J. (2004). Development of MITC Isotropic Triangular Shell Finite Elements , Computers and Structures, 82(11-12): 945-962 .
29.
Nayak, A.K. , Moy, S.S.J. and Shenoi, R.A. (2002). Free Vibration Analysis of Composite Sandwich Plates based on Reddy’s Higher Order Theory , Composites Part B, Engineering, 33: 505-519 .
30.
Nayak, A.K. , Shenoi, R.A. and Moy, S.S.J. (2002). Analysis of Damped Composite Sandwich Plates using Plate Bending Elements with Substitute Shear Strain Fields based on Reddy’s Higher-order Theory , Proc. Inst. Mech. Engg., Part C, Journal of Mech. Engg. Science, 216: 591-606 .
31.
Nayak, A.K. , Shenoi, R.A. and Moy, S.S.J. (2004). Transient Response of Composite Sandwich Plates , Composite Structures, 64: 249-267 .
32.
Nayak, A.K. , Moy, S.S.J. and Shenoi, R.A. (2003). Quadrilateral Finite Elements for Multi-layer Sandwich Plates , Journal of Strain Analysis for Engineering Design, 38: 377-394 .
33.
Dvorkin, E.N. and Bathe, K.J. (1984). A Continuum Mechanics based Four-node Shell Element for General Non-linear Analysis , Engineering Computations, 1: 77-88 .
34.
Huang, H.C. and Hinton, E. (1984). A Nine Node Lagrangian Mindlin Plate Element with Enhanced Shear Interpolation , Engineering Computations, 1: 369-379 .
35.
Rao, V.S. , Shankar, B.V. and Sun, C.T. (1992). Constrained Layer Damping of Initially Stressed Composite Beams using Finite Elements . Journal of Composite Materials, 26(12): 1752-1766 .
36.
Vinson, J.R. (2001). Sandwich Structures, Applied Mechanics Reviews , Transactions of The American Society of Mechanical Engineers, 54: 201-214 .
37.
Batoz, J.L. , Bathe, K.J. and Ho, L.W. (1980). A Study of Three-node Triangular Plate Bending Elements , Int. J. Num. Meth. Engg., 15, 1771-1812 .
38.
Jeyachandrabose, C. , Kirkhope, J. and Babu, C.R. (1985). An Alternative Explicit Formulation for the DKT Plate Bending Element , Int. J. Num. Meth. Engg., 21(7): 1289-1293 .
39.
Robinson, J. and Haggenmacher, G. (1979). Lora-An Accurate Four Nodes Stress Plate Bending Element , Int. J. Num. Meth. Engg., 14(2): 296-306 .
40.
Batoz, J.L. (1982). An Explicit Formulation for an Efficient Triangular Plate-bending Element , Int. J. Num. Meth. Engg., 18: 1077-1089 .
