Isogeometric analysis for nonlinear buckling of FGM plates under various types of thermal gradients

Abstract

This study attempts at analyzing buckling responses of functionally graded material (FGM) plates under diverse types of thermal loadings. An accurate and effective numerical approach based on isogeometric analysis (IGA) to predict the nonlinear thermal buckling behavior is developed. A refined higher-order shear deformation theory (HSDT) which accounts for the geometric nonlinearity in the von Kármán sense is presented and used to derive the equilibrium and governing equations for FGM plate in thermal environments. Two different types of transverse shear functions are considered in the refined HSDT. IGA uses non-uniform rational B-spline (NURBS) basis functions which enable to accomplish easily the smoothness of arbitrary continuity order. Thus, the present method satisfies the C1-continuity of the displacement field required by the proposed HSDT. Several numerical examples involving buckling behavior of various kinds of FGM plates subjected to uniform, linear and nonlinear temperature distributions across the thickness are simulated, and the results are compared to the analytical solutions for the verification purpose. Parametric studies are also carried out on FGM plates under the different through-thickness temperature variations to scrutinize the thermal buckling features. Temperature gradient through the thickness by the one-dimensional (1-D) heat conduction and thermal profile developed by the three-dimensional (3-D) heat conduction are also taken into account. Results demonstrate that the proposed IGA method can be used as an accurate and effective numerical tool for analyzing the thermal buckling responses of FGM plates, and the 3-D heat conduction needs to be considered in the buckling analysis of FGM plates subjected to thermal conduction.