0
TECHNICAL PAPERS

Exact Solution for Simply Supported and Multilayered Magneto-Electro-Elastic Plates

[+] Author and Article Information
E. Pan

Structures Technology, Inc. 543 Keisler Drive, Suite 204, Cary, NC 27511e-mail: pan@ipass.net

J. Appl. Mech 68(4), 608-618 (Jan 30, 2001) (11 pages) doi:10.1115/1.1380385 History: Received April 02, 2000; Revised January 30, 2001
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.

References

Ochoa, O. O., and Reddy, J. N., 1992, Finite Element Analysis of Composite Laminates, Kluwer, Boston, MA.
Pagano,  N. J., 1969, “Exact Solutions for Composites in Cylindrical Bending,” J. Compos. Mater., 3, pp. 398–411.
Pagano,  N. J., 1970, “Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates,” J. Compos. Mater., 4, pp. 20–34.
Srinivas,  S., Rao,  C. V. J., and Rao,  A. K., 1969, “Flexure of Simply Supported Thick Homogeneous and Laminated Rectangular Plates,” Z. Angew. Math. Mech., 49, pp. 449–458.
Srinivas,  S., and Rao,  A. K., 1970, “Bending, Vibration and Buckling of Simply Supported Thick Orthotropic Rectangular Plates and Laminates,” Int. J. Solids Struct., 6, pp. 1463–1481.
Pan,  E., 1991, “An Exact Solution for Transversely Isotropic, Simply Supported and Layered Rectangular Plates,” J. Elast., 25, pp. 101–116.
Gilbert,  F., and Backus,  G., 1966, “Propagator Matrices in Elastic Wave and Vibration Problems,” Geophysics, 31, pp. 326–332.
Noor,  A. K., and Burton,  W. S., 1990, “Three-Dimensional Solutions for Antisymmetrically Laminated Anisotropic Plates,” ASME J. Appl. Mech., 57, pp. 182–188.
Ray,  M. C., Rao,  K. M., and Samanta,  B., 1992, “Exact Analysis of Coupled Electroelastic Behavior of a Piezoelectric Plate under Cylindrical Bending,” Comput. Struct., 45, pp. 667–677.
Ray,  M. C., Bhattacharya,  R., and Samanta,  B., 1993, “Exact Solutions for Static Analysis of Intelligent Structures,” AIAA J., 31, pp. 1684–1691.
Heyliger,  P., and Brooks,  S., 1996, “Exact Solutions for Laminated Piezoelectric Plates in Cylindrical Bending,” ASME J. Appl. Mech., 63, pp. 903–910.
Heyliger,  P., 1997, “Exact Solutions for Simply Supported Laminated Piezoelectric Plates,” ASME J. Appl. Mech., 64, pp. 299–306.
Bisegna,  P., and Maceri,  F., 1996, “An Exact Three-Dimensional Solution for Simply Supported Rectangular Piezoelectric Plates,” ASME J. Appl. Mech., 63, pp. 628–638.
Lee,  J. S., and Jiang,  L. Z., 1996, “Exact Electroelastic Analysis of Piezoelectric Laminae via State Space Approach,” Int. J. Solids Struct., 33, pp. 977–990.
Vel,  S. S., and Batra,  R. C., 2000, “Three-Dimensional Analytical Solution for Hybrid Multilayered Piezoelectric Plates,” ASME J. Appl. Mech., 67, pp. 558–567.
Berlincourt,  D. A., Curran,  D. R., and Jaffe,  H., 1964, “Piezoelectric and Piezomagnetic Materials and Their Function in Transducers,” Phys. Acoust., 1, pp. 169–270.
Landau, L. D., and Lifshitz, E. M., 1984, Electrodynamics of Continuous Media, 2nd Ed., Rev. and Enlarged by E. M. Lifshitz and L. P. Pitaevskii, Pergamon Press, New York.
Avellaneda,  M., and Harshe,  G., 1994, “Magnetoelectric Effect in Piezoelectric/Magnetostrictive Multiplayer (2-2) Composites,” J. Intell. Mater. Syst. Struct., 5, pp. 501–513.
Harshe,  G., Dougherty,  J. P., and Newnham,  R. E., 1993, “Theoretical Modeling of Multilayer Magnetoelectric Composites,” Int. J. Appl. Electromagn. Mater., 4, pp. 145–159.
Nan,  C. W., 1994, “Magnetoelectric Effect in Composites of Piezoelectric and Piezomagnetic Phases,” Phys. Rev. B, B50, pp. 6082–6088.
Benveniste,  Y., 1995, “Magnetoelectric Effect in Fibrous Composites With Piezoelectric and Piezomagnetic Phases,” Phys. Rev. B, B51, pp. 16424–16427.
Huang,  J. H., 1998, “Analytical Predictions for the Magneto-Electric Coupling in Piezomagnetic Materials Reinforced by Piezoelectric Ellipsoidal Inclusions,” Phys. Rev. B, B58, pp. 12–15.
Li,  J., and Dunn,  M. L., 1998, “Anisotropic Coupled-Field Inclusion and Inhomogeneity Problems,” Philos. Mag. A, A77, pp. 1341–1350.
Li,  J., and Dunn,  M. L., 1998, “Micromachanics of Magnetoelectroelastic Composite Materials: Average Fields and Effective Behavior,” J. Intell. Mater. Syst. Struct., 9, pp. 404–416.
Stroh,  A. N., 1958, “Dislocations and Cracks in Anisotropic Elasticity,” Philos. Mag., 3, pp. 625–646.
Ting, T. C. T., 1996, Anisotropic Elasticity, Oxford University Press, Oxford, UK.
Ting,  T. C. T., 2000, “Recent Developments in Anisotropic Elasticity,” Int. J. Solids Struct., 37, pp. 401–409.
Pan,  E., 1997, “A General Boundary Element Analysis of 2-D Linear Elastic Fracture Mechanics,” Int. J. Fract., 88, pp. 41–59.
Kausel,  E., and Roesset,  J. M., 1981, “Stiffness Matrices for Layered Soils,” Bull. Seismol. Soc. Am., 71, pp. 1743–1761.
Datta, S. K., 2000, “Wave Propagation in Composite Plates and Shells,” Comprehensive Composite Materials, Vol. 1, A. Kelly and C. Zweben, eds., Elsevier, New York, pp. 511–558.
Pan,  E., 1997, “Static Green’s Functions in Multilayered Half Spaces,” Appl. Math. Modelling, 21, pp. 509–521.
Pan,  E., and Datta,  S. K., 1999, “Ultrasonic Waves in Multilayered Superconducting Plates,” J. Appl. Phys., 86, pp. 543–551.
Timoshenko, S., and Woinowsky-Krieger, S., 1987, Theory of Plates and Shells, McGraw-Hill, New York.
Smittakorn,  W., and Heyliger,  P. R., 2000, “A Discrete-Layer Model of Laminated Hygrothermopiezoelectric Plates,” Mechanics of Composite Materials and Structures, 7, pp. 79–104.
Huang,  J. H., and Kuo,  W. S., 1997, “The Analysis of Piezoelectric/Piezomagnetic Composite Materials Containing Ellipsoidal Inclusions,” J. Appl. Phys., 81, pp. 1378–1386.

Figures

Grahic Jump Location
Variation of the electric displacement Dx(=Dy) along the thickness direction in a homogeneous and piezoelectric plate caused by an internal load on the middle plane and a surface load on the top surface
Grahic Jump Location
Variation of the stress component σzz along the thickness direction in a homogeneous and piezoelectric plate caused by an internal load on the middle plane and a surface load on the top surface
Grahic Jump Location
Variation of the electric potential ϕ along the thickness direction in the sandwich piezoelectric/piezomagnetic plate caused by a surface load on the top surface
Grahic Jump Location
Variation of the magnetic potential ψ along the thickness direction in the sandwich piezoelectric/piezomagnetic plate caused by a surface load on the top surface
Grahic Jump Location
Variation of the electric displacement Dx(=Dy) along the thickness direction in the sandwich piezoelectric/piezomagnetic plate caused by a surface load on the top surface
Grahic Jump Location
Variation of the electric displacement Dz along the thickness direction in the sandwich piezoelectric/piezomagnetic plate caused by a surface load on the top surface
Grahic Jump Location
Variation of the magnetic induction Bx(=By) along the thickness direction in the sandwich piezoelectric/piezomagnetic plate caused by a surface load on the top surface
Grahic Jump Location
Variation of the magnetic induction Bz along the thickness direction in the sandwich piezoelectric/piezomagnetic plate caused by a surface load on the top surface
Grahic Jump Location
Variation of the normal stress σzz along the thickness direction in the sandwich piezoelectric/piezomagnetic plate caused by a surface load on the top surface.
Grahic Jump Location
Variation of the elastic displacement ux(=uy) along the thickness direction in a homogeneous and piezoelectric plate caused by an internal load on the middle plane and a surface load on the top surface

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In