A new $${\varvec{n}}$$th-order shear deformation theory for isogeometric thermal buckling analysis of FGM plates with temperature-dependent material properties

Abstract

This study presents an isogeometric analysis (IGA) for investigating the buckling behavior of functionally graded material (FGM) plates in thermal environments. The material properties of the FGM plate are considered to be graded across the thickness, and temperature dependency of the material properties is taken into account. A new nth-order shear deformation theory with the von Karman type of geometric nonlinearity, in which the optimum order number to best approximate the thermal buckling problem can be chosen, is developed. The principle of virtual work is used to derive the governing equations for the nonlinear thermal buckling analysis. The nth-order shear deformation theory is incorporated into the non-uniform rational B-spline-based IGA which fulfills the $$C^{1}$$ -continuity requirement of the proposed higher-order plate theory. The discrete nonlinear system equations are solved by utilizing the modified Newton–Raphson iterative technique. Parametric studies on the buckling behavior of FGM plates subjected to diverse through-thickness temperature variations are performed, and the influence of temperature dependency of the material properties is examined. Results validate the performance accuracy and effectiveness of the proposed IGA based on the nth-order shear deformation theory, and they demonstrate that temperature-dependent material properties should be included in the thermal buckling analysis.