Refined zigzag theory for homogeneous, laminated composite, and sandwich plates: a homogeneous limit methodology for zigzag function selection

The Refined Zigzag Theory (RZT) for homogeneous, laminated composite, and sandwich plates is revisited to offer a fresh insight into its fundamental assumptions and practical possibilities. The theory is introduced from a multi-scale formalism starting with the in plane displacement field expressed as a superposition of coarse and fine contributions. The coarse displacement field is that of first-order shear deformation theory, whereas the fine displacement field has a piecewise linear zigzag distribution through the thickness. The resulting (cinematic field provides a more realistic representation of the deformation states of transverse-shear-flexible plates than other similar theories. The condition of limiting homogeneity of transverse-shear properties is proposed and yields four distinct sets of zigzag functions. Analytic solutions for highly heterogeneous sandwich plates undergoing elasto-static deformations are used to identify the best performing zigzag functions. Unlike previously used methods, which often result in anomalous conditions and nonphysical solutions, the present theory does not rely on transverse-shear-stress equilibrium constraints. For all material systems, there are no requirements for use of transverse-shear correction factors to yield accurate results. To model homogeneous plates with the frill power of zigzag kinematics, infinitesimally small perturbations in the transverse shear properties are derived, thus enabling highly accurate predictions of homogeneous plate behavior without the use of shear correction factors. The RZT predictive capabilities to model highly heterogeneous sandwich plates are critically assessed, demonstrating its superior efficiency, accuracy, and a wide range of applicability. The present theory, which is derived from the virtual work principle, is well-suited for developing computationally efficient C°-continuous finite elements, and is thus appropriate for the analysis and design of high performance load-bearing aerospace structures.