Geometrically nonlinear analysis of functionally graded plates with symmetrical parabolic thickness profile under uniaxial compression based on isogeometric analysis

Abstract

This paper is dedicated to the study of geometrically nonlinear behaviour of variable thickness functionally graded plates subjected to uniaxial compressive forces. The plate’s geometry in this study could have either uniform thickness or symmetrical parabolic-form thickness. To develop the theoretical formulation of the problem, the kinematics of the plates are described by the third-order shear deformation theory for plate structures with thin and moderate thickness. The geometrical nonlinearity is accounted for by von Karman’s assumptions, while the rule of mixture is used to evaluate the effective material properties of functionally graded materials whose constituent phases vary across the plate’s thickness. The governing equation is derived via the principle of virtual work with assumptions of small-strain problems. The Isogeometric Analysis is then used to discretize the governing equations. Arc-length iterative technique with imperfection is used to trace the equilibrium paths of the problem. Various numerical examples are also performed to validate the accuracy of the proposed numerical model and investigate the nonlinear response of the variable thickness functionally graded plates.