This study presents a higher-order zigzag theory (HOZT) for the static bending analysis of laminated composite and sandwich plates under sinusoidally distributed transverse loading. The formulation superimposes higher-order through-thickness displacement polynomials onto the Murakami Zigzag Function (MZF), extending the simplified kinematics of Ali et al. [29], originally restricted to symmetric cross-ply laminates, to a unified framework for general lamination schemes. Transverse shear stresses are recovered through equilibrium-based integration, and analytical solutions are obtained via Navier’s method for simply supported plates. The present formulation offers three principal advances. First, the higher-order zigzag kinematics are systematically applied, within a single formulation, to symmetric and anti-symmetric cross-ply, symmetric and anti-symmetric angle-ply, arbitrary unsymmetric, and sandwich configurations. Second, compared with Murakami’s zigzag theory (MZT) and the Enhanced Refined Zigzag Theory (Enhanced-RZT), which employ linear zigzag enrichment only, the present higher-order terms provide substantially improved accuracy for thick laminates. For a four-layer anti-symmetric cross-ply plate at \(a/h=4\) , errors in the in-plane displacement \(u_2\) are reduced from approximately \(61\%\) to below \(4.5\%\) , while errors in \(\sigma _{yy}\) decrease from over \(22\%\) to below \(1\%\) . Third, the model captures through-thickness displacement asymmetry induced by unsymmetric stacking sequences and surface loading, effects that conventional HSDT and FSDT formulations cannot reproduce. A key limitation is also identified and quantified: Because the MZF depends solely on geometric layer distribution, accuracy deteriorates for highly heterogeneous sandwich plates, with transverse displacement errors reaching approximately \(48\%\) . This observation provides motivation for the development of constitutively consistent higher-order zigzag theories. Comprehensive numerical studies across diverse thickness ratios, anisotropy levels, and layer counts confirm the superior predictive capability of the proposed model.
