Size-dependent behaviour of in-plane bi-directional functionally graded porous microplates with variable thickness based on the modified strain gradient theory and IGA

• The isogeometric analysis is once again proved as an efficient numerical method • The influence of porosity on the classical model is lower than size-dependent models • The size-dependent effect has a significant influence on the mechanical responses • Considering high-order boundary conditions eliminates some mode shapes • The thickness variations play an important role on results of size-dependent models In this paper, the isogeometric analysis (IGA) is extended to study the size-dependent behaviour of bending, buckling and free vibration of in-plane bi-directional functionally graded porous microplates with variable thickness. In order to capture the effect of size, the modified strain gradient elasticity theory, which has three length scale parameters, is used. Regarding to the third-order shear deformation theory, the equations of motions are derived by using the Hamilton's principle and then are discretised based on the IGA approach. The material properties vary continuously through in-plane directions by employing the rule of mixture and the porosity distribution is considered an even type. The C 2 -continuity requirement can be easily achieved by increasing the order of the non-uniform rational B-spline (NURBS) basis functions larger than two. The influences of the size effect, aspect ratios, boundary conditions, thickness variations, material gradations, and porosity distributions on the deflections, the fundamental natural frequencies, and the buckling load values of the rectangular, circular and elliptical microplates are studied. The obtained results are compared with the previously published studies to show the performance and efficiency of the present research.