In this research, the general governing set of differential equations for axisymmetric thick FG pressurized cylinders with exponential function of material properties is derived based on third order shear deformation theory. Afterwards, a general analytical solution of governing equations based on Eigen values problems is conducted for cylinders under clamped ends condition. Furthermore, a numerical modeling is done in order to compare the results of two different solution and prove the accuracy of analysis. The displacements and stresses resulted from FEM and TSDT are depicted for a case study along the radial and longitudinal direction of the cylinder. Afterwards, the effect of internal and external pressure, FGM inhomogeneity constants and higher order approximation is investigated. The results of SDT and FEM show good agreement and prove the fact that usage of FGM cylinders causes lower values of displacements and stresses.
Using the third-order shear deformation theory (TSDT), an analytical solution for deformations and stresses of axisymmetric clamped-clamped thick cylindrical shells made of functionally graded material (FGM) subjected to internal pressure and thermal loading are presented. The material properties are graded along the radial direction according to power functions of the radial direction. It is assumed that Poisson's ratio is constant across the cylinder thickness. The differential equations governing were generally derived, making use of TSDT. Following that, the set of non-homogenous linear differential equations for the cylinder with clamped-clamped ends was solved, and the effect of loading and supports on the stresses and displacements was investigated. The problem was also solved, using the finite element method (FEM), and the results of which were compared with those of the analytical method. Furthermore, the effect of increases in the temperature gradient on displacement and stress values has been studied. Finally, in order to investigate the effect of third-order approximations on displacements and stresses, a comparison between the results of first-and third-order shear deformation theory has been made.
In this paper, nonlinear analysis of thick cylindrical shells with arbitrary variable thickness made of hyperelastic FGM with radially variation of material properties in nearly incompressible state under non-uniform pressure loading is presented. Thickness and pressure of the shell vary in axial direction by linear and/or nonlinear functions. The governing equilibrium equations are derived based on shear deformation theory (SDT). The Mooney-Rivlin type material is considered which is a suitable hyperelastic model for rubbers. Boundary Layer Method of the perturbation theory which is known as Matched Asymptotic Expansion (MAE) is used for solving the governing equations. A new ingenious solution and formulation have been defined during current study to simplify and abbreviate the representation of inner and outer equations components in MAE. In order to validate the results of the current analytical solution, a numerical modeling based on Finite Element Method (FEM) have been investigated. Afterwards, for different rubber case studies, the effect of material constants, inhomogeneity index, geometry and pressure profiles on displacements, stresses and hydrostatic pressure distributions resulting from MAE and FEM solution have been illustrated. This approach enables insight into the nature of the deformation and stress distribution across the wall of rubber vessels and offers the potential for investigating the mechanical functionality of blood vessels such as arteries in physiological pressure range. The results prove the effectiveness of SDT and MAE combination to derive and solve the governing equations of nonlinear problems such as nearly incompressible hyperelastic FG shells.
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