In this article, static and dynamic responses of cross-ply bi-stable composite plates were studied. To accurately predict the natural frequencies and snap-through load, a set of higher order shape functions were proposed. In static analysis, the stable configurations, the deflection of corners, and the midpoint of the plate were calculated. For dynamic analysis, Hamilton’s principle is used to provide approximate solutions to the vibration problem under study. The responses of the plate under ramp and harmonic applied forces were determined, the effect of shape functions on the prediction of the first natural frequency of the plate and the required force for snap-through were investigated. A finite element model is also developed to study the static and vibration characteristics of bi-stable composite plate. The qualitative and quantitative comparisons between the finite element method results and those obtained from the present analysis are generally good and satisfactory. The developed analytical model can also be used for parametric study and further design modification.
HyerMW. Some observations on the cured shape of thin unsymmetric laminates. J Compos Mater1981; 15: 175–194.
2.
HyerMW. Calculations of the room-temperature shapes of unsymmetric laminates. J Compos Mater1981; 15: 296–310.
3.
HyerMW. The room-temperature shapes of four-layer asymmetric cross-ply laminates. J Compos Mater1982; 16: 318–340.
4.
HamamotoAHyerMW. Non-linear temperature-curvature relationships for unsymmetric graphite-epoxy laminates. Int J Solids Struct1987; 23: 919–935.
5.
JunWJHongCS. Effect of residual shear strain on the cured shape of unsymmetric cross-ply thin laminates. Compos Sci Technol1990; 38: 55–67.
6.
JunWJHongCS. Cured shape of unsymmetric laminates with arbitrary lay-up angles. Reinf Plast Compos World1992; 11: 1352–1366.
7.
SchlechtMSchulteKHyerMW. Advanced calculations of the room-temperature shapes of thin unsymmetric composite laminates. Compos Struct1995; 32: 627–633.
8.
DanoMHyerMW. Thermally-induced deformation behavior of unsymmetric laminates. Int J Solids Struct1998; 35: 2101–2120.
9.
GiddingsPFBowenCRSaloAIT. Bistable composite laminates: effects of laminate composition on cured-shape and response to thermal load. Compos Struct2010; 92: 2220–2225.
10.
BettsDNSaloAITBowenCR. Characterisation and modeling of the cured shapes of arbitrary layup bistable composite laminates. Compos Struct2010; 92: 1694–1700.
11.
PirreraAAvitabileDWeaverPM. Bistable plates for morphing structures: A refined analytical approach with high-order polynomials. Int J Solids Struct2010; 47: 3412–3425.
12.
MooreMZiaei-RadSSalehiH. Thermal response and stability characteristics of bi-stable composite laminates by considering temperature dependent material properties and resin layers. Appl Compos Mater2013; 20: 87–106.
13.
MooreMZiaei-RadSFirouzian-NejadA. Temperature-curvature relationships in asymmetric angle ply laminates by considering the effects of resin layers and temperature dependency of material properties. J Compos Mater2014; 48: 1071–1089.
14.
MattioniFWeaverPMFriswellMI. Multistable composite plates with piecewise variation of lay-up in the planform. Int J Solids Struct2009; 46: 151–164.
15.
SchultzMRHyerMWWilliamsRB. Snap through of unsymmetric laminates using piezocomposite actuators. Compos Sci Technol2006; 66: 2442–2448.
16.
PortelaPMCamanhoPPWeaverPM. Analysis of morphing multistable structures actuated by piezoelectric patches. Comput Struct2008; 86: 347–356.
17.
GiddingsPFBowenCRButlerR. Characterization of actuation properties of piezoelectric bi-stable carbon-fibre laminates. Compos Part A2008; 39: 697–703.
18.
FernandesAMauriniCVidoliS. Multiparameter actuation for shape control of bistable composite plates. Int J Solids Struct2010; 47: 1449–1458.
19.
DanoMLHyerMW. Snap-through of unsymmetric fiber-reinforced composite laminates. Int J Solids Struct2002; 39: 175–198.
20.
DanoMLHyerMW. SMA-induced snap-through of unsymmetric fiber-reinforced composite laminates. Int J Solids Struct2003; 40: 5949–5972.
21.
PotterKWeaverPMSemanAA. Phenomena in the bifurcation of unsymmetric composite plates. Compos Part A2007; 38: 100–106.
TawfikSAStefan DancilaDArmaniosE. Planform effects upon the bistable response of cross-ply composite shells. Compos Part A2011; 42: 825–833.
24.
ZhangZWuHHeX. The bistable behaviors of carbon fiber/epoxy anti-symmetric composite shells. Compos Part B2013; 47: 190–199.
25.
ZhangZWuHYeG. Systematic experimental and numerical study of bistable snap processes for anti-symmetric cylindrical shells. Compos Struct2014; 112: 368–377.
26.
ArrietaAFNeildSAWaggDJ. On the cross-well dynamics of a bi-stable composite plate. J Sound Vib2011; 330: 3424–3441.
27.
ArrietaAFNeildSAWaggDJ. Nonlinear dynamic response and modeling of a bi-stable composite plate for applications to adaptive structures. Nonlinear Dyn2009; 58: 259–272.
FuhongDHaoLShanyiD. A multi-stable wavy skin based on bi-stable laminates. Compos Part A2013; 45: 102–108.
31.
FuhongDHaoLShanyiD. A multi-stable lattice structure and its snap-through behavior among multiple states. Compos Struct2013; 97: 56–63.
32.
ArrietaAFBilgenOFriswellMI. Modelling and configuration control of wing-shaped bi-stable piezoelectric composites under aerodynamic loads. Aerosp Sci Technol2013; 29: 453–461.
33.
ReddyJN. Mechanics of laminated composite plates and shells: theory and analysis, 2nd ed. Boca Raton, London, New York, Washington D.C: CRC Press LLC, 2004.
34.
KyriazoglouCGuildFJ. Finite element prediction of damping of composite GFRP and CFRP laminates - a hybrid formulation - vibration damping experiments and Rayleigh damping. Compos Sci Technol2006; 66: 487–498.
