Abstract
In this paper geometrically nonlinear theories of laminated composite plates with piezoelectric laminae are developed. The formulations are based on thermopiezoelectricity, and include the coupling between mechanical deformations, temperature changes, and electric displacements. Two different theories are presented: one based on an equivalent-single-layer third-order theory and the other based on the layerwise theory, both of which were developed by the senior author for composite laminates without piezoelectric laminae. In the present study, they are extended to include piezoelectric laminae. In both theories, the electric field is expanded layerwise through the laminate thickness. The dynamic version of the principle of virtual displacements (or Hamilton’s principle) is used to derive the equations of motion and associated boundary conditions of the two theories. These theories may be used to accurately determine the response of laminated plate structures with piezoelectric laminae and subjected to thermomechanical loadings.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Browning C E, Husman G E, Whitney J M 1977 Moisture effects in epoxy matrix composites.Composite materials: Testing and design, Fourth conference ASTM STP 617, pp. 481–496
Carslaw H S, Jaeger J C 1959Conduction of heat in solids 2nd edn (London: Oxford University Press)
Chandra R, Chopra I 1993 Structural modelling of composite beams with induced-strain actuators.AIAA J. 31: 1692–1701
Crawley E, de Luis J 1987 Use of piezoelectric actuators as elements of intelligent structures.AIAA J. 25: 1373–1385
Eringen A C 1963 On the foundations of electrostatics.Int. J. Eng. Sci. 1: 127–153
Jost W 1952Diffusion in solids, liquids, and gases (New York: Academic Press)
Lee C K 1990 Theory of laminated piezoelectric plates for the design of distributed sensors/actuators: Part I: Governing equations and reciprocal relationships.J. Acoust. Soc. Am. 97: 1144–1158
Mitchell J A, Reddy J N 1994 A refined hybrid plate theory for composite laminates with piezoelectric laminae. Department of Mechanical Engineering, Texas A & M University, College Station, Texas AlsoInt. J. Solids Struct. 32: 2345–2367 (1995)
Nelson D F 1978 Theory of nonlinear electrostatics of dielectric, piezoelectric crystals.J. Acoust. Soc. Am. 63: 1738–1748
Nowinski J L 1978Theory of thermoelasticity with applications (Alphen aan den Rijn, The Netherlands: Sijthoff & Noordhoff)
Nye J F 1957Physical properties of crystals (Cambridge: Oxford University Press)
Pai P F, Nayfeh A H, Oh K, Mook D T 1993 A refined nonlinear model of composite plates with integrated piezoelectric actuators and sensors.Int. J. Solid Struct. 30 (12): 1603–1630
Penfield P Jr, Hermann A H 1967 Electrodynamics of moving media. Research Monograph No. 40, Cambridge, Massachusetts
Reddy J N 1984aEnergy and variational methods in applied mechanics (New York: John Wiley & Sons)
Reddy J N 1984b A simple higher-order theory for laminated composite plates.J. Appl. Mech. 51: 745–752
Reddy J N 1987 A generalization of two-dimensional theories of laminated composite plates.Commun. Appl. Numer. Meth. 3: 173–180
Reddy J N 1993An introduction to the finite element method 2nd edn (New York: McGraw-Hill)
Reddy J N 1995Theory and analysis of laminated composite plates and shells (New York: John Wiley & Sons) (to be published)
Reddy J N, Gartling D K 1994The finite element method in heat transfer and fluid dynamics (Boca Raton, Fl: CRC Press)
Reddy J N, Robbins D H Jr 1994 Theories and computational models for composite laminates.Appl. Mech. Rev. 47 (6): 147–169
Robbins D H Jr, Reddy J N 1993 Modelling of thick composites using a layerwise laminate theory.Int. J. Numer. Meth. Eng. 36: 655–677
Shen C H, Springer G S 1976 Moisture absorption and desorption of composite materials.J. Compos. Mater. 10: 2–20
Tiersten H F 1964 Coupled magnetomechanical equations for magnetically saturated insulators.J. Math. Phys. 5: 1298–1318
Tiersten H F 1969Linear piezoelectric plate vibrations (New York: Plenum)
Tiersten H F 1971 On the nonlinear equations of thermoelectroelasticity.Int. J. Eng. Sci. 9: 587–604
Tiesten H F 1981 Electroelastic interactions and the piezoelectric equations.J. Acoust. Soc. Am. 70: 1567–1576
Tiersten H F 1993a Electroelastic equations for electroded thin plates subjected to large driving voltages.J. Appl. Phys. 74: 3389–3393
Tiersten H F 1993b Equations for the extension and flexure of relatively thin electroelastic plates undergoing large electric fields.Mechanics of electromagnetic materials and structures (eds) J S Lee, G A Maugin, Y Shindo (New York: The American Society of mechanical Engineers) AMD-vol. 161, 21–34
Toupin R A 1956 The elastic dielectric.J. Rational Mech. Anal. 5: 849–916
Tzou N S, Zhong J P 1993 Electromechanics and vibrations of piezoelectric shell distributed systems.J. Dyn. Syst., Meas. Control 115: 506–517
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Reddy, J.N., Mitchell, J.A. On refined nonlinear theories of laminated composite structures with piezoelectric laminae. Sadhana 20, 721–747 (1995). https://doi.org/10.1007/BF02823215
Issue Date:
DOI: https://doi.org/10.1007/BF02823215