A coupled zigzag theory for the dynamics of piezoelectric hybrid cross-ply plates

Abstract

A recently developed coupled third-order zigzag theory for the statics of piezoelectric hybrid crossply plates is extended to dynamics. The theory combines a third-order zigzag approximation for the in-plane displacements and a sub-layerwise linear approximation for the electric potential, considering all components of the electric field. The nonuniform variation of the transverse displacement due to the piezoelectric field is accounted for. The conditions for the absence of shear traction at the top and bottom surfaces and continuity of transverse shear stresses in the presence of electromechanical loading are satisfied exactly, thereby reducing the number of displacement variables to five, which is the same as in a first-or third-order equivalent single-layer theory. The governing equations of motion are derived from the extended Hamilton's principle. The theory is assessed by comparing the Navier solutions for the free and forced harmonic vibration response of simply supported plates with the exact three-dimensional piezoelasticity solutions. Comparisons for hybrid test, composite and sandwich plates establish that the present theory is quite accurate for the dynamic response of moderately thick plates.

An efficient C0 FE model for the analysis of composites and sandwich laminates with general layup

“…Cho et al [5] have also presented coupled zigzag theory for hybrid plates under thermoelectric load considering global variation for the deflection and a layerwise linear variation of electric potential, which are inadequate to capture the layerwise distribution of deflection due to thermal and potential fields. Kapuria et al [16,17] have presented zigzag theory for hybrid beams and plates in which number of variable are reduced to FSDT by satisfying interface and boundary conditions, it yield approximately accurate results for cross ply only. Wu et al [33] proposed C 0 type higher-order theory for bending analysis of laminated composite and sandwich plates.…”

Assessment of improved zigzag and smeared theories for smart cross-ply composite cylindrical shells including transverse normal extensibility under thermoelectric loading

“…Among them, the equivalent single layer (ESL) theories like the classical laminate theory (CLT) [2], the first-order shear deformation theory (FSDT) [3], and the refined third-order theory (TOT) [4] are the most computationally efficient ones, with layer-independent number of primary displacement variables. But, previous studies [5] have shown that the single global variation across the thickness, which is assumed for the displacements in these theories, is not able to capture the effect of large layerwise inhomogeneity in thermal, mechanical, and electric properties in the hybrid laminates. The layerwise theories (LWT) [6] considering layerwise linear variation of inplane displacements are very accurate, but these are computationally unattractive for practical design problems since the number of unknown variables is proportional to the number of layers in the laminate.…”

“…The layerwise theories (LWT) [6] considering layerwise linear variation of inplane displacements are very accurate, but these are computationally unattractive for practical design problems since the number of unknown variables is proportional to the number of layers in the laminate. The zigzag theories (ZIGT) have been developed [5,7,8] as an efficient alternative to the LWTs, wherein the inplane displacements are initially assumed to contain a combination of global and layerwise terms, but the number of mechanical variables is reduced to that of an ESL theory by enforcing the conditions on transverse shear stresses at layer interfaces, and top and bottom surfaces.…”

A new zig-zag theory and C0 plate bending element for composite and sandwich plates

“…By adding a local linear zig-zag function to the global third-order displacement field, the higher order zig-zag theories considering transverse normal strain have been presented to predict the displacements and stresses of thick smart laminated plate under mechanical, thermal, and electric loads [14]. In addition to the aforementioned zig-zag theories, Kapuria [15] and Kapuria et al [16,17] also developed the zig-zag theories to analyze the static and the dynamic behaviors of laminated composite plates. More discussion on the zig-zag theories can be found in the article [18][19][20].…”