Static and dynamic nonlinear stability analyses of hybrid sandwich composite beams under variable in-plane loads

Post-buckling and dynamic nonlinear stability analyses of a sandwich functionally graded material (FGM) composite beam subject to in-plane compressive static and periodic loading are conducted by implementing a higher-order shear deformation with von Karman kinematics. The dynamic instability region is evaluated using the Mathieu-Hill-type equation in Bolotin’s method. Comparisons of the layered composite beam, FGM sandwich composite beam, shape memory polymer (SMP) composite beam, and SMP-FGM sandwich composite beam with variable in-plane loads (Nx1,Nx2,Nx3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(N_x^1, N_x^2, N_x^3)$$\end{document} are depicted for the first time in the current work. The unstable region of Nx3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_x^3$$\end{document} is lower compared with those of Nx1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_x^1$$\end{document} and Nx2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_x^2$$\end{document}.