Isogeometric approach for nonlinear bending and post-buckling analysis of functionally graded plates under thermal environment

TL;DR

This paper develops an isogeometric analysis method for nonlinear bending and post-buckling of functionally graded plates under thermal effects, incorporating higher-order shear deformation theory and temperature-dependent material properties.

Contribution

It introduces a NURBS-based isogeometric finite element formulation for FGM plates considering thermal effects and nonlinear behavior, with detailed analysis of various influencing factors.

Findings

The approach accurately predicts nonlinear bending and buckling behavior.

Material property variation and temperature distribution significantly affect plate stability.

Numerical results validate the effectiveness of the proposed method.

Abstract

In this paper, equilibrium and stability equations of functionally graded material (FGM) plate under thermal environment are formulated based on isogeometric analysis (IGA) in combination with higher-order shear deformation theory (HSDT). The FGM plate is made by a mixture of two distinct components, for which material properties not only vary continuously through thickness according to a power-law distribution but also are assumed to be a function of temperature. Temperature field is assumed to be constant in any plane and uniform, linear and nonlinear through plate thickness, respectively. The governing equation is in nonlinear form based on von Karman assumption and thermal effect. A NURBS-based isogeometric finite element formulation is utilized to naturally fulfil the rigorous C1-continuity required by the present plate model. Influences of gradient indices, boundary conditions, temperature distributions, material properties, length-to-thickness ratios on the behaviour of FGM plate are discussed in details. Numerical results demonstrate excellent performance of the present approach.