A new zig-zag coupled theory is developed for hybrid cross-ply plates with some piezoelectric layers using third-order zig-zag approximation for the inplane displacements and sublayer wise piecewise linear approximation for the electric potential. The theory considers all electric field components and can model open and closed-circuit boundary conditions. The deflection field accounts for the transverse normal strain due to the piezoelectric $d33$ coefficient. The displacement field is expressed in terms of five displacement variables (which are the same as in FSDT) and electric potential variables by satisfying exactly the conditions of zero shear stresses at the top and bottom, and their continuity at layer interfaces. The governing equations are derived from the principle of virtual work. Comparison of the Navier solutions for the simply-supported plates with the analytical three-dimensional piezoelasticity solutions establishes that the present efficient zig-zag theory is quite accurate for moderately thick plates.

# A Coupled Zig-Zag Third-Order Theory for Piezoelectric Hybrid Cross-Ply Plates

Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the Applied Mechanics Division, February 5, 2003; final revision, October 17, 2003. Associate Editor: R. C. Benson. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Journal of Applied Mechanics, Department of Mechanical and Environmental Engineering, University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication in the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.

*J. Appl. Mech*. Sep 2004, 71(5): 604-614 (11 pages)

**Published Online:**November 9, 2004

Kapuria, S. (November 9, 2004). "A Coupled Zig-Zag Third-Order Theory for Piezoelectric Hybrid Cross-Ply Plates ." ASME. *J. Appl. Mech*. September 2004; 71(5): 604–614. https://doi.org/10.1115/1.1767170

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