Nonlinear bending analysis of variable thickness multi-directional functionally graded plates based on isogeometric analysis

Abstract

In this study, the nonlinear bending behavior of multi-directional functionally graded plates with variable thickness is investigated. To this regard, the governing equation of the plate problem is developed based on the principle of virtual work, while the third-order shear deformation plate theory proposed by Reddy is employed to describe the kinematic relations. The geometrical nonlinearity is taken into account by adopting the von Kármán’s assumptions for nonlinear problems with small strains and moderate rotations. The plates investigated in this study are assumed to be made from two different material constituents, whose volume fractions vary spatially within the plate domain. The effective material properties are calculated based on the mixture approach. The Isogeometric Analysis approach is used as a numerical method to solve the governing equations. NURBS basis functions are used as interpolation functions for geometrical modeling and discretization procedure, where the C 1-continuity requirement is meet efficiently. Various numerical examples are conducted to validate the accuracy of the proposed approach and investigate the influences of geometrical and material factors on the nonlinear bending responses of the plates.