Abstract
A new analytical solution is presented for functionally graded (FG) beams to investigate the bending behaviour under hygro-thermo-mechanical loading using a new fifth order shear and normal deformation theory (FOSNDT). The material properties of the FG beam are varied along the thickness direction according to the power law index. In the present theory, a polynomial shape function is expanded up to fifth-order in terms of thickness coordinate to consider the effects of transverse shear and normal deformations. The present theory is free from the shear correction factor. Using the Navier’s solution technique the closed-form solution is obtained for simply supported FG beams. All the results are presented in non-dimensional form and validated it by developing the classical beam theory (CBT), first order shear deformation theory (FSDT by Mindlin) and third order shear deformation theory (TSDT by Reddy) considering the hygro-thermo-mechanical loading effects which is mostly missing in the literature. It is noticed that the presented FOSNDT is very simple and accurate to predict the bending behaviour of FG beams under linear and non-linear hygro-thermo-mechanical loadings.
Highlights
The composites are usually a mixture of two or more than two materials in combination
functionally graded (FG) beams are even most suitable to resist hygro stresses generally developed in seashore and marine structures located in humid environment
The main focus of the present study is to investigate the bending behaviour of FG beam using fifth order shear and normal deformation theory under the non-linear hygro-thermo-mechanical loadings
Summary
The composites are usually a mixture of two or more than two materials in combination. The main aim of this study is to present the bending analysis of FG beams considering the linear and non-linear variations of hygro-thermo-mechanical loadings. The hygro-thermo-mechanical analysis for the FG plate is studied by Zidi et al [101], Zenkour et al [97], Daouadji et al [32], Zenkour and Radwan [86] and Sayyad and Ghugal [98] using different higher order theories and mathematical approaches. The main focus of the present study is to investigate the bending behaviour of FG beam using fifth order shear and normal deformation theory under the non-linear hygro-thermo-mechanical loadings. The top surface of the FG beam is made up of metal, whereas the bottom surface is made up of ceramic material
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