Bending analysis of functionally graded plates under mechanical and thermal environment using non-polynomial shear deformation theory

In this paper, a penalty-based C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C<^>{0}$$\end{document} finite element (FE) model for C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C<^>{1}$$\end{document} higher-order shear deformation theory (HSDT) five variables is proposed for linear bending analysis of functionally graded material (FGM) plates under mechanical and thermal loads. The rule of mixture is considered to model the material characteristics of the FGM. The principle of virtual work is utilized to obtain the weak form of governing equations for finite element formulation. A C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C<^>{0}$$\end{document} finite element mode is formulated using seven degrees-of-freedom per node to discretized the finite element mesh. The performance of proposed model is assessed by validation and comparison with available solutions in the literature. A parametric study is carried out to study the effect of design and material parameters such as material variation, side-to-thickness ratio, and aspect ratio of FGM plates. Further, a comparative study has been made between third-order shear deformation theory (TSDT) and a non-polynomial shear deformation theory (NPSDT). The present study provides a clear understanding of linear bending analysis of FGM plates.