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Abstract

The effects of accurately accounting for transverse shear strain, transverse normal strain, and discrete layer kinematics on the computed global response of actuated plates are investigated using a hierarchical displacement-based, two-dimensional (2-D) finite element model that is developed specifically for composite laminates. The hierarchical model is used to obtain the first-order shear deformation model, a higher-order cubic equivalent-singlelayer model, a type-I layerwise model, and a type-II layerwise model as special cases. Each of the first three models uses a reduced constitutive matrix that is based on the assumption of zero transverse normal stress; however, the models differ significantly in their assumed distribution of transverse shear strain. The type-II layerwise model utilizes a full 3-D constitutive matrix and includes both discrete layer transverse shear effects and discrete layer transverse normal effects. The scope of the study is restricted to homogeneous plates with surface-mounted actuators covering a wide range of span-to-thickness ratios. The results clearly demonstrate that as the span-to-thickness ratio of the actuated region decreases, discrete layer kinematics become very important for accurately characterizing the global response of the actuated plate. The set of laminate kinematic assumptions utilized by a particular model influence the predicted global response primarily through the so-called local kinematic effect where a portion of the available actuation energy is diverted to the production of localized transverse shear deformation and localized transverse normal deformation in the vicinity of the actuator edges, thereby reducing the amount of actuation energy that is available for producing the intended global deformation mode.

Keywords

actuated plates laminate models transverse shear deformation finite elements

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References

Benjeddou, A. 2000. ‘‘Advances in Piezoelectric Finite Element Modeling of Adaptive Structural Elements: A Survey’’ , Computers and Structures, 76: 347–363 .

Chattopadhyay, A. , Li, J. and Gu, H. 1999. ‘‘Coupled Thermo-Piezoelectric-Mechanical Model for Smart Composite Laminate’’ , AIAA Journal, 37(12): 1633–1638 .

Chopra, I. 2002. ‘‘Review of State of Art of Smart Structures and Integrated Systems’’ , AIAA Journal, 40(11): 2145–2187 .

Crawley, E.G. and de Luis, J. 1987. ‘‘Use of Piezoelectric Actuators as Elements of Intelligent Structures’’ , AIAA Journal, 25: 1373–1385 .

Gopinathan, S.V. , Varadan, V.V. and Varadan, V.K. 2000. ‘‘A Review and Critique of Theories for Piezoelectric Laminates’’ , Smart Materials and Structures, 9: 24–48 .

Heyliger, P. 1997. ‘‘Exact Solutions for Simply Supported Laminated Piezoelectric Plates’’ , Journal of Applied Mechanics, 64: 299–306 .

Heyliger, P. , Ramirez, G. and Saravanos, D.A. 1994. ‘‘Coupled Discrete Layer Finite Elements for Laminated Piezoelectric Plates’’ , Communications in Numerical Methods in Engineering, 10: 971–981 .

Kim, J. , Varadan, V.V. and Varadan, V.K. 1996a. ‘‘Finite Element Modeling of Structures Including Piezoelectric Active Devices’’ , International Journal for Numerical Methods in Engineering, 40: 1–16 .

Kim, J. , Varadan, V.V. , Varadan, V.K. and Bao, X.Q. 1996b. ‘‘Finite-Element Modeling of a Smart Cantilever Plate and Comparison with Experiments’’ , Smart Materials and Structures, 5: 165–170 .

10.

Lee, C.K. 1990. ‘‘Theory of Laminated Piezoelectric Plates for the Design of Distributed Sensors/Actuators. Part I: Governing Equations and Reciprocal Relationships’’ , Journal of the Acoustic Society of America, 87(3): 1144–1158 .

11.

Lee, H.J. and Saravanos, D.A. 1997. ‘‘Generalized Finite Element Formulation for Smart Multilayered Thermal Piezoelectric Composite Plates’’ , International Journal of Solids and Structures, 34(26): 3355–3371 .

12.

Lin, C.C. , Hsu, C.Y. and Huang, H.N. 1996. ‘‘Finite Element Analysis on Deflection Control of Plates with Piezoelectric Actuators’’ , Composite Structures, 35: 423–433 .

13.

Miller, S.E. and Abramovich, H. 1995. ‘‘A Self-Sensing Piezolaminated Actuator Model for Shells using a First-order Shear Deformation Theory’’ , Journal of Intelligent Material Systems and Structures, 6: 624–638 .

14.

Reddy, J.N. 1987. ‘‘A Generalization of Two-dimensional Theories of Laminated Composite Plates’’ , Communications in Applied Numerical Methods, 3: 173–180 .

15.

Reddy, J.N. 1989. ‘‘On the Generalization of Displacement-based Laminate Theories’’ , Applied Mechanics Reviews, 42(11), Part 2, S213–S222 .

16.

Robbins, Jr., D.H. and Reddy, J.N. 1991. ‘‘Finite Element Analysis of Piezoelectrically Actuated Beams’’ , Computers and Structures, 41(2): 265–279 .

17.

Robbins, Jr., D.H. and Reddy, J.N. 1993. ‘‘Modelling of Thick Composites Using a Layerwise Laminate Theory’’ , International Journal for Numerical Methods in Engineering, 36: 655–677 .

18.

Robbins, Jr., D.H. and Reddy, J.N. 1996a. ‘‘An Efficient Computational Model for the Stress Analysis of Smart Plate Structures’’ , Smart Materials and Structures, 5(3): 353–360 .

19.

Robbins, Jr., D.H. and Reddy, J.N. 1996b. ‘‘Variable Kinematic Modelling of Laminated Composite Plates’’ , International Journal for Numerical Methods in Engineering, 39: 2283–2317 .

20.

Saravanos, D.A. 1997. ‘‘Mixed Laminate Theory and Finite Element for Smart Piezoelectric Composite Shell Structures’’ , AIAA Journal, 35: 1327–1333 .

21.

Saravanos, D.A. and Heyliger, P.R. 1995. ‘‘Coupled Layerwise Analysis of Composite Beams with Embedded Piezoelectric Sensors and Actuators’’ , Journal of Intelligent Material Systems and Structures, 6(3) 350–363 .

22.

Saravanos, D.A. , Heyliger, P.R. and Hopkins, D.A. 1997. ‘‘Layerwise Mechanics and Finite Element for the Dynamic Analysis of Piezoelectric Composite Plates’’ , International Journal of Solids and Structures, 34(3): 359–378 .

23.

Tzou, H.S. and Gadre, M. 1989. ‘‘Theoretical Analysis of a Multilayered Thin Shell Coupled with Piezoelectric Shell Actuators for Distributed Vibration Controls’’ , Journal of Sound and Vibration, 132(3): 433–450 .

24.

Zhou, X. , Chattopadhyay, A. and Gu, H. 2000. ‘‘Dynamic Response of Smart Composites Using a Coupled Thermo-Piezoelectric-Mechanical Model’’ , AIAA Journal, 38(10): 1939–1948 .

The Effect of Laminate Kinematic Assumptions on the Global Response of Actuated Plates

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