A Multi-scale Refined Zigzag Theory for Multilayered Composite and Sandwich Plates with Improved Transverse Shear Stresses

The Refined Zigzag Theory (RZT) enables accurate predictions of the in-plane displacements, strains, and stresses. The transverse shear stresses obtained from constitutive equations are layer-wise constant. Although these transverse shear stresses are generally accurate in the average, layer-wise sense, they are nevertheless discontinuous at layer interfaces, and thus they violate the requisite interlaminar continuity of transverse stresses. Recently, Tessler applied Reissner's mixed variational theorem and RZT kinematic assumptions to derive an accurate and efficient shear-deformation theory for homogeneous, laminated composite, and sandwich beams, called RZT(m), where "m" stands for "mixed". Herein, the RZT(m) for beams is extended to plate analysis, where two alternative assumptions for the transverse shear stresses field are examined: the first follows Tessler's formulation, whereas the second is based on Murakami's polynomial approach. Results for elasto-static simply supported and cantilever plates demonstrate that Tessler's formulation results in a powerful and efficient structural theory that is well-suited for the analysis of multilayered composite and sandwich panels.