A refined size-dependent couple stress theory for laminated composite micro-plates using isogeometric analysis

In this article, a refined modified couple stress theory based on isogeomeric analysis to capture the small-scale effect on laminated composite micro-plates is developed for the first time. Based on Hamilton's principle, the weak form for composite plate is established by using the Reddy's third order shear deformation theory without shear correction factor and the refined modified couple stress theory. Unlike the modified couple stress theory, which contains only one material length scale parameter, the proposed theory contains three material length scale parameters. To confirm the accuracy of the proposed method, several examples are presented, discussed and compared to references' solutions. In addition, cut-out complicated shapes are analyzed to show the influences of the small-scale effect on free vibration behaviors of laminated micro-plates. An increase in the material length scale parameter leads to decrease in the deflection, stresses and increase in frequencies and critical buckling load factor. The presented numerical results show the great efficiency of the NURBS-based isogeometric analysis for capturing the small-scale effect of the composite laminated micro-plates.