Size-dependent analysis of homogeneous and functionally graded microplates using IGA and a non-classical Kirchhoff plate theory

The paper presents an effective thin plate formulation based on isogeometric analysis (IGA) and a non-classical Kirchhoff plate theory to study static bending, free vibration, and buckling behaviors of homogeneous and functionally graded microplates. The small scale effects are captured using a non-classical Kirchhoff plate theory which is developed based on a modified couple stress theory. The requirement for C1-continuity in terms of the non-classical Kirchhoff plate theory is straightforwardly possessed with the aid of inherent high-order continuity of non-uniform rational B-spline (NURBS). Studies on convergence and comparison with reference solutions are demonstrated in order to show the effectiveness and accuracy of the proposed method. Numerical examples are presented to illustrate the effects of small scale on the mechanical response of homogeneous and functionally graded microplates. The results reveal that the small scale effects lead to a reduction of deflection and an increase in frequency and buckling loads because of an increase in plate stiffness, and more importantly the small scale effects are significant for the thin plates.