Size-dependant behaviour of functionally graded microplates based on the modified strain gradient elasticity theory and isogeometric analysis

•A robust numerical model is proposed for functionally graded microplates.•The size effect is captured using the strain gradient theory.•Governing equations are solved using Isogeometric Analysis (IGA) approach.•Verification is performed for both rectangular and circular microplates.•The effect of small-scale on the behavior of microplates is investigated. This paper presents a robust numerical model, which takes into account both size-dependent and shear deformation effects, for the bending, buckling and free vibration analyses of functionally graded microplates. The size-dependent effect is captured by using the modified strain gradient elasticity theory with three length scale parameters, whilst the shear deformation effect is accounted by using the third-order shear deformation theory. The rule of mixture is employed to describe the distributions of material phrases through the plate thickness. By using Hamilton’s principle, the governing equations are derived and then discretized by employing an Isogeometric Analysis (IGA) approach, where the Non-Uniform Rational B-Splines (NURBS) basis functions are adopted to meet the C2-continuity requirement. Physical mesh convergence and verification studies are performed to prove the accuracy and reliability of the present model. In addition, parametric studies are also carried out to investigate the size effect in conjunction with the influences of gradient index, shear deformation effect and boundary conditions on the responses of microplates.