Post-buckling and Large-deflection analysis of a sandwich FG plate with FG porous core using Carrera’s Unified Formulation

Abstract

Abstract In this study, the unified formulation of a full geometrically nonlinear refined plate theory in a total Lagrangian approach is developed to study the post-buckling and large-deflection analysis of sandwich functionally graded (FG) plate with FG porous (FGP) core. The plate has three layers so that the upper and lower layers are FG and the middle layer (core) is the FGP, which is considered with four cases in terms of the porosity core distribution. The different two-dimensional (2D) plate structures kinematics are consistently implemented based on the Carrera’s Unified Formulation (CUF) by means of an index notation and an arbitrary expansion function of the generalized variables in the thickness direction, leading to lower- to higher-order plate models with only pure displacement variables. Furthermore, a finite element approximation and the principle of virtual work are used to easily and straightforwardly formulate the nonlinear governing equations in a total Lagrangian manner, whereas a path-following Newton-Raphson linearization scheme based on the arc-length constraint is utilized to solve the full geometrically nonlinear problem. Numerical assessments are finally conducted to confirm the capabilities of the proposed CUF plate model to predict the post-buckling and large-deflection equilibrium curves with high accuracy.