Analysis of FGM micro cylindrical shell with variable thickness using Cooper Naghdi model: Bending and buckling solutions

Abstract

Functionally graded materials (FGMs) due to high thermal and mechanical resistance have a special applications in the aerospace industry, nuclear reactors and electronic and magnetism industries. In the present study, the bending and buckling analysis of cylindrical micro shell with variable thickness made of FGMs based on modified couple stress theory (MCST) are presented. In this theory, the effect of material length scale parameter is considered. Power law distribution is used to distribute FGMs and the mechanical properties of micro shell vary in thickness direction. The displacement field follows the Cooper-Naghdi model and the governing equations of equilibrium are obtained analytically using the energy method. Nonlinear equations of cylindrical micro shell with variable thickness for clamped-clamped boundary conditions are solved numerically by differentially quadrature method (DQM). The effect of various mechanical parameters, micro shell dimensional proportions, material length scale parameter, also the effect of the distribution of FGMs on deflection and critical buckling load of the cylindrical micro shell with variable thickness have been investigated. A brief summary of the results of the present study will show that increasing the material length scale parameter increases the critical buckling load, and decrease the deflection of the cylindrical micro shell with variable thickness. Increasing the power distribution of FGMs increases critical buckling load, which is vice versa for the deflection of micro shell.