Abstract
The investigation being reported is concerned with the development and applications of a layerwise hybrid strain based lower-order flat triangular laminated composite shell finite element with distributed piezoelectric components. This shell element has three nodes and is formed by stacking a lower-order flat triangular shell element with piezoelectric effects. In every node there are seven degrees of freedom (dof). These include three translational dof, three rotational dof, and one electric potential dof. The important drilling dof (ddof) is included in every node. The degenerated three dimensional solid assumption and the first order shear deformation theory (FSDT) were adopted. Thus, shear and membrane lockings are eliminated. This feature is superior to those elements applying the displacement formulation. Explicit expressions for the consistent element mass and stiffness matrices as well as loading vectors were obtained by using the symbolic algebraic package, MAPLE V so that it reduces considerably the computational time as opposed to those employing numerical matrix inversion and numerical integration for the derivation of element matrices. Computed results for static and free vibration analysis of a bimorph beam with sensors and actuators, and a semi-circular cylindrical laminated composite ring with piezoelectric components are included to demonstrate the efficiency and accuracy of the present shell finite element.
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References
Allik, H. and Hughes, T.J.R. (1970), “Finite element method for piezoelectric vibration”, Int. J. Num. Meth. Eng. 2, 151–157.
Tzou, H.S. and Tseng, C.I. (1990), “Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: a piezoelectric finite element approach”, J. Sound and Vibration 138, 17–34.
Robbins, D.H. and Reddy, J.N. (1991), “Analysis of piezoelectrically actuated beams using a layer-wise displacement theory”, Computers and Structures 41, 265–279.
Hwang, W.S. and Park, H.C. (1993), “Finite element modeling of piezoelectric sensors and actuators”, A.LA.A. Journal 31, 930–937.
Heyliger, P. and Ramirez, G. (1994), “Coupled discrete-layer finite elements for laminated piezoelectric plates”, Communications in Numerical Methods for Engineering 10, 971–981.
Carrera, E. (1997), “An improved Reissner-Mindlin-type model for the electromechanical analysis of multilayered plates including piezo-layers”, J. of Intell. Mat. Syst. Struct. 8, 232–248.
Lammering, R. (1990), “The application of a finite shell element for composites containing piezo-electric polymers in vibration control”, Computers and Structures 41, 1101–1109.
Tzou, H.S. and Tseng, C.I. (1988), “Active vibration controls of distributed parameters system by finite element method”, Computers in Engineering 3, 599–604.
Tzou, H.S. and Ye, R. (1996), “Analysis of piezoelastic structures with laminated piezoelectric triangular shell elements”, A.I.A.A. J. 34, 110–115.
To, C.W.S. and Liu, M.L. (1994), “Hybrid strain based three-node flat triangular shell elements”, Finite Elements in Analysis and Design 17, 169–203.
Liu, M.L. and To, C.W.S. (1994), “Vibration analysis of structures by hybrid strain based three-node flat triangular shell elements”, Journal of Sound and Vibration 184 (5), 801–821.
To, C.W.S. and Wang, B. (1998), “Hybrid strain based three-node flat triangular laminated composite shell elements”, Finite Elements in Analysis and Design 28, 177–207.
Liu, W. (2000), Finite Element Modeling of Laminated Plates and Shells with Distributed Piezoelectric Components, M.Sc. Thesis, University of Nebraska, Lincoln, Nebraska.
Wang, B. (1995), Finite Element Analysis of Geometrically Nonlinear Laminated Composite Shell Structures, Ph.D. Thesis, University of Western Ontario, London, Ontario, Canada.
Bailey, T. and Hubbar, J.E., Jr. (1985), “Distributed piezoelectric-polymer active vibration control of a cantilever beam”, Journal of Guidance, Control and Dynamics 8, 605–611.
To, C.W.S. and Liu, W. (2001), “Hybrid strain based finite element modeling of laminated plates with distributed piezoelectric components”, Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, September 9–12, Pittsburgh, PA, Paper No. DETC2001/CIE-21275.
Tseng, C.I. (1989), Electromechanical Dynamics of A Coupled Piezoelectric/Mechanical System Applied to Vibration Control and Distributed Sensing, Ph.D. Thesis, University of Kentucky, Lexington, KY.
Lee, J.K. and Marcus, M.A. (1981), “The deflection-bandwidth product of polyvinylidene fluoride benders and related structures”, Ferroelectrics 32, 93–101.
Tzou, H.S. (1988), “Development of a light-weight robot end-effector using polymer piezoelectric bimorph”, in Proceedings 1989 IEEE International Conference on Robotics and Automation 3, 1704–1709.
Lee, C.K. and Moon, F.C. (1989), “Laminated piezopolymer plates for torsion and bending sensors and actuators”, Journal of the Acoustical Society of America 85, 2432–2439.
Chen, C.Q., Wang, X.M. and Shen, Y.P. (1996), “Finite element approach of vibration control using self-sensing piezoelectric actuators”, Computers and Structures 60, 505–512.
Chen, S.H., Wang, Z.D. and Liu, X.H. (1997), “Active vibration control and suppression for intelligent structures”, Journal of Sound and Vibration 200 (2), 167–177.
Suleman, A. and Venkayya, V.B. (1995), “A simple finite element formulation for a laminated composite plate with piezoelectric layers”, J. of Intell. Mat. Syst. Struct. 6, 776–782.
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To, C.W.S., Liu, W. (2003). Analysis of Laminated Composite Shell Structures with Piezoelectric Components. In: Yang, J.S., Maugin, G.A. (eds) Mechanics of Electromagnetic Solids. Advances in Mechanics and Mathematics, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0243-8_15
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DOI: https://doi.org/10.1007/978-1-4613-0243-8_15
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