Thermo-mechanical bending analysis of micro/nano-laminated plates using an enhanced zigzag theory and new modified couple stress model

Abstract

Micro- and nano-scale laminated composites are central to MEMS, soft robotics, and 3D-printed systems, yet their reliability hinges on accurately predicting size-dependent responses to coupled thermo-mechanical loads. This paper introduces a unified formulation that integrates the Enhanced Refined Zigzag Theory (ERZT) with the New Modified Couple Stress Theory (NMCST) for the thermo-mechanical bending of these structures. The proposed framework captures both the through-thickness zigzag displacement pattern and the size effect for cross-ply, angle-ply, and sandwich laminates. A characteristic feature of the model is the post-processing of the transverse shear stresses through the 3D equilibrium equations, which guarantees interfacial continuity. The governing equations are derived from the principle of virtual work and solved by Navier’s method for simply supported boundary conditions. In the classical limit (l/h → 0) the model is validated against the 3D thermal-elasticity solutions from existing literature, showing excellent agreement for displacements, in-plane stresses, and transverse shear stresses. Parametric studies then illustrate the size-dependent stiffening predicted by the NMCST, quantifying how the aspect ratio a/h and the dimensionless length-scale ratio l/h jointly govern the deflection and stress amplitudes. This model couples ERZT kinematics with NMCST under combined transverse mechanical and through-thickness thermal loads, capturing for the first time the size-dependent thermo-mechanical bending of cross-ply, angle-ply, and sandwich micro-/nano-laminates. The resulting tool is computationally efficient and provides a robust methodology for the design of high-performance micro/nano-structured components in aerospace and biomedical applications.