An inverse-hyperbolic zig-zag theory in refined couple stress framework for laminated and sandwich microplates

An analytical framework is proposed for the bending and buckling analysis of laminated composite and sandwich microplates, combining the refined couple-stress theory (RCST) with the non-polynomial inverse-hyperbolic zig-zag theory. The primary goal of this study is to provide a theoretical framework that enables the simultaneous modeling of size effects, transverse shear deformation, and interlaminar stress continuity. For the first time, the non-polynomial zig-zag theory is extended to the analysis of laminated microplates in the size-dependent continuum approach. Additionally, the size-dependent behavior of laminated sandwich microplates is studied for the first time using the RCST. The governing equations are derived using the principle of virtual work, which are solved analytically using Navier’s closed-form solution under simply supported boundary conditions. The accuracy of the proposed formulation is demonstrated by validating the results against the existing literature using other shear-deformation theories, including zig-zag theories. A parametric study is conducted to investigate the effects of size dependency, transverse shear deformation, and loading conditions on the bending and buckling behavior of the laminated composite structures. The proposed model provides a high-fidelity, efficient, and physically consistent analytical tool for the analysis of laminated composite and sandwich microplates, offering significant improvements over classical and existing higher-order theories.