A smoothed Zig-Zag plate finite element for the analysis of laminated composite plates

This paper presents an alternative plate finite element to simulate the mechanical behavior of laminated composite plates using the Positional Finite Element Method (PFEM). Based on the Zig-Zag Theory (ZZT), a Reissner–Mindlin kinematics is enhanced with piecewise linear functions of in-plane displacement, creating a zig-zag profile across the thickness. Cauchy's theorem and the longitudinal equilibrium of layers are applied to enforce the interlaminar continuity of transverse shear stresses. The resulting shear strain field is integrated along the thickness, leading to a piecewise third-order displacement function that replaces the former linear profile. The proposed kinematics, named Smoothed Zig-Zag Theory (SZZT), is layer-independent and can be calibrated to better fit the problem. A cubic-order plate finite element with ten degrees of freedom per node is formulated based on SZZT to directly predict through-the-thickness displacements and stresses in laminated plate structures. Different configurations of isotropic and orthotropic cross-ply laminated plates are investigated. The static response of SZZT is compared with exact solutions and finite element results available in the literature.