A size-dependent zigzag model for composite laminated micro beams based on a modified couple stress theory

Abstract

This study developed a new composite laminated size-dependent beam model based on a re-modified couple stress theory and a refined zigzag theory. Unlike the classical theory, the proposed model only includes one internal material length scale parameter and can capture the scale effects. In addition, the current model satisfies a priori interlaminar continuity conditions and can accurately predict the displacements and stresses, particularly the interlaminar stresses. Reissner’s Mixed Variational Theorem is employed to derive the equilibrium equations and related boundary conditions. Numerical examples of simply supported cross-ply beams subjected to transverse sinusoidal loads are analytically solved by directly applying the derived formulas. The results prove that this model can be applied to investigate the scale effects, which increase the stiffness and decrease the displacements and stresses. Moreover, the results obtained with present model are compared with the exact solutions to validate the present formulation.