Size-dependent nonlinear bending behavior of porous FGM quasi-3D microplates with a central cutout based on nonlocal strain gradient isogeometric finite element modelling

Abstract

With the aid of the non-uniform rational B-spline (NURBS)-based isogeometric technique, for the first time, the size-dependent geometrically nonlinear bending characteristics of microplates made of porous functionally graded materials (FGMs) having a central cutout with different shapes are studied. The nonlocal strain gradient continuum elasticity within the framework a hybrid higher-order quasi-3D plate theory is adopted to describe the kinematic relations via only four unknowns. To capture the effective material properties, a porosity-dependent rule of mixture is employed. The nonlocal strain gradient nonlinear load-deflection responses are obtained corresponding to various geometrical and material parameters as well as different boundary conditions. It is revealed that the significance of both the nonlocal and strain gradient reduces. This prediction is the same for all values of the material property gradient index as well as the porosity index. Also, it is demonstrated that a central cutout leads to change the trend of load-deflection response, and this change occurs at a specific value for the applied distributed load which depends on several parameters such as the cutout geometry and boundary conditions. In addition, it is displayed that corresponding to different maximum deflections, the significance of the strain gradient size effect in the absence of nonlocality on the nonlinear flexural stiffness of a porous FGM microplate is more than that of the nonlocal size effect in the absence of the strain gradient size dependency.