Nonlinear static and transient isogeometric analysis of functionally graded microplates based on the modified strain gradient theory

The objective of this study is to develop an effective numerical model within the framework of an isogeometric analysis (IGA) to investigate the geometrically nonlinear responses of functionally graded (FG) microplates subjected to static and dynamic loadings. The size effect is captured based on the modified strain gradient theory with three length scale parameters. The third-order shear deformation plate theory is adopted to represent the kinematics of plates, while the geometric nonlinearity is accounted based on the von Kármán assumption. Moreover, the variations of material phrases through the plate thickness follow the rule of mixture. By using Hamilton’s principle, the governing equation of motion is derived and then discretized based on the IGA technique, which tailors the non-uniform rational B-splines (NURBS) basis functions as interpolation functions to fulfil the C²-continuity requirement. The nonlinear equations are solved by the Newmark’s time integration scheme with Newton-Raphson iterative procedure. Various examples are also presented to study the influences of size effect, material variations, boundary conditions and shear deformation on the nonlinear behaviour of FG microplates.