An investigation of modified couple stress theory in buckling analysis of micro composite laminated Euler–Bernoulli and Timoshenko beams

Buckling analysis of composite laminated beams is developed based on modified couple stress theory. By applying principle of minimum potential energy and considering two different beam theories, i.e., Euler–Bernoulli and Timoshenko beam theories, governing equations, boundary and initial conditions are derive for micro composite laminated beams. By using the new curvature tensor and modified couple stress theory, the size effects are captured unlike the classical continuum theories. A model of simply supported composite laminated beams is considered. These models can cover the classical composite beam theories and isotropic beam theories. Governing equations are solved by utilizing the Fourier series expansions. Comparison between results obtained by present study and those obtained by literature reveals that they are in good agreement. Some numerical results are presented to study the effect of material length scale parameter, beam thickness and length of beam on the micro composite laminated beam behavior. In addition, to investigate the effect of lamination on the buckling analysis of micro composite laminated beams, two types of lamination, i.e., [0, 90, 0] and [90, 0, 90] are considered.