A couple stress model in non-polynomial framework to examine structural responses of laminated composite micro-plates: An analytical solution

In the present article, the couple stress models in the non-polynomial framework are developed and employed to examine the structural response characteristics of composite micro-plates. The length scale effects in the micro-laminates are considered using the couple stress theory. The trigonometric, inverse-trigonometric, hyperbolic, inverse-hyperbolic and exponential shear shape functions are considered to model transverse shear deformation effects in micro-plates. The Hamilton principle is employed to formulate the governing equations assuming linear structural kinematics. The governing equations are solved for simply supported micro-plates using the Navier solution for the prediction of analytical results. The structural responses of the composite micro-plates are examined for bending, free vibration, and buckling responses. The nondimensionalized deflection, stresses, frequencies, and axial buckling loads are evaluated using the present methodology. The higher buckling modes and free vibration modes are also obtained. The response characteristics due to five plate theories are compared and the applicability of the considered transverse shear deformation theories to model and analyze composite micro-plates is assessed. The effects of various parameters on the structural responses of micro-laminates are examined.

Automated summary

In this article, couple stress models in the non-polynomial framework are developed and used to examine the structural response characteristics of composite micro-plates. The study considers length scale effects and various shear shape functions to model transverse shear deformation effects, with governing equations formulated using the Hamilton principle and linear structural kinematics. The methodology is applied to analyze bending, free vibration, and buckling responses of the micro-plates, with comparisons made among different plate theories to assess the applicability of various deformation theories in modeling composite micro-plates.