Static and vibration analysis of functionally graded microplate with porosities based on higher-order shear deformation and modified strain gradient theory

Based on fundamental equations of the elasticity theory, a unified higher-order shear deformation theory is developed for bending and free vibration analysis of functionally graded (FG) microplates with porosities. The modified strain gradient theory is employed to capture the size effects. Bi-directional series with hybrid shape functions are used to solve the problems. Several important effects including thickness-to-material length scale parameters, side-to-thickness ratio, and boundary conditions on the deflections and natural frequencies of FG porous microplates are investigated.