Nonlinear thermo-mechanical isogeometric analysis of axially functionally graded porous graphene platelet-reinforced composite arches resting on Winkler–Pasternak foundation

Abstract

This paper delves into the investigation of the nonlinear thermal vibration and buckling responses of the axially functionally graded porous graphene platelet-reinforced composite (AFGP-GPLRC) semi-elliptic and parabolic arches resting on the Winkler–Pasternak foundation. Concurrently, three different length-wise GPL dispersion patterns mixed with three thickness-wise porosity distribution patterns are considered. The effective thermo-mechanical properties of the AFGP-GPLRC arch are calculated within the framework of the modified Halpin–Tsai parallel model and the Gaussian random field model. A theoretical framework that encompasses the third-order shear deformation theory (TSDT) in conjunction with the non-uniform rational B-splines (NURBS)-based isogeometric analysis (IGA) approach for the AFGP-GPLRC arch is introduced. Hamilton’s principle and TSDT formulation are implemented to formulate the governing equation of motion associated with nonlinear thermo-mechanical analysis. By virtue of the NURBS-based IGA technique and the direct iterative method, the nonlinear frequency is obtained. The current theoretical framework is thoroughly validated through a rigorous comparison of the numerical solutions against existing benchmark results. Parametric analyses, considering components such as GPL reinforcements, porosity imperfections, foundation parameters, and thermal gradients, delve into their influence on the nonlinear thermal vibration and buckling responses of the AFGP-GPLRC arch. These studies are elucidated through a series of demonstrative examples that vividly portray the interplay of these variables.