Torsional buckling response of FG porous thick truncated conical shell panels reinforced by GPLs supporting on Winkler elastic foundation

In the present research, torsional buckling response of thick truncated conical shell panels supporting on Winkler-type elastic medium has been surveyed. The shell is constructed from a porous metal material reinforced by graphene platelets (GPLs) in which the porosity and volume weight fraction of nanofillers are graded along the thickness of shell. Three functions for porosity distribution and five patterns of GPLs are examined. To estimate the Young modulus of the shell, Tsai-Halpin micromechanical model, and for its mass density, extended rule of mixture is employed. Linear theory of 3D elasticity in conjunction with the virtual work principle and numerical graded finite element method (FEM) are applied to derive the state of equilibrium in pre-buckling mode. Torsional buckling forces are derived by applying nonlinear Green strains and by deriving geometric stiffness matrix of the system. The effect of various parameters such as coefficient of porosity, various distributions of porosity and different nanofiller patterns, weight fraction of graphene nanofillers, semi vertex angle of cone, span angle, stiffness of elastic medium and various boundary conditions on torsional buckling loads of functionally graded (FG) porous truncated conical panel reinforced by GPLs have been presented. The main purpose of this research is obtaining the best distribution of porosity and GPLs pattern and investigating the influence of adding nano particles on the torsional buckling forces of the shell. Results denote that employing GPL-X pattern in conjunction with porosity distribution 1 provides the maximum value of buckling loads. Besides by adding the nano particles, the amount of buckling loads will increase 100%.