This article introduces a novel mixed method that combines the Fast Fourier Transform technique and a conventional Finite Element Method for investigating thermo-mechanical behavior of a thick functionally graded cylinder under asymmetric loadings. Material properties are assumed to vary along the radial direction according to a power function. Thermo-elastic governing equations of the cylinder are derived using principle of virtual work in cylindrical coordinates. Plane strain assumption is considered for a long cylinder during the analysis. Fast Fourier Transform technique is utilized in circumferential direction to discretize equations and related boundary conditions. Finite element method is then applied to remaining equations. For convergence study, the results obtained from this method are compared with those extracted from exact and complete FE solutions. It is observed from the results that the method has a super algebraic convergence behavior in circumferential direction. Influence of the mesh refinement is also investigated in the radial direction. According to ability of the mixed FFT-FE method for asymmetric analyzing, two kinds of loadings are considered here and results are presented. In thermo-elastic analyzing of the long cylinder, it’s obvious that the present method benefits from some features such as fast convergence and low computational cost in comparison with FE solution. پرونده مقاله

In this paper, thermo-elastic analysis of a rotating thick truncated conical shell subjected to the temperature gradient, internal pressure and external pressure is presented. Given the existence of shear stress in the conical shell due to thickness change along the axial direction, the governing equations are obtained based on first-order shear deformation theory (FSDT). These equations are solved by using multi-layer method (MLM). The model has been verified with the results of finite element method (FEM). Finally, some numerical results are presented to study the effects of thermal and mechanical loading, geometry parameters of truncated conical shell. پرونده مقاله

A semi-analytical iterative method as one of the newest analytical methods is used for the elastic analysis of thick-walled spherical pressure vessels made of functionally graded materials subjected to internal pressure. This method is accurate, fast and has a reasonable order of convergence. It is assumed that material properties except Poisson’s ratio are graded through the thickness direction of the sphere according to an exponential distribution. For different values of inhomogeneity constant, distributions of radial displacement, radial stress, circumferential stress, and von Mises equivalent stress, as a function of radial direction, are obtained. A numerical solution, using finite element method (FEM), is also presented. Good agreement was found between the semi-analytical results and those obtained through FEM. پرونده مقاله

In the present work, a study of thermoelastic analysis of a rotating thick truncated conical shell subjected to the temperature gradient and non-uniform internal pressure is carried out. The formulation is based on first-order shear deformation theory (FSDT), which accounts for the transverse shear. The governing equations, derived using minimum total potential energy principle, are solved, using multi-layered method (MLM). The model has been verified with the results of finite element method (FEM) for several tapering angles of the truncated cone. The numerical results obtained are presented graphically and the effects of thermal and mechanical loading, tapering angle of truncated cone, and profile of internal pressure are studied in detail. پرونده مقاله

Time-dependent creep analysis is presented for the calculation of stresses and displacements of axisymmetric thick-walled cylindrical pressure vessels made of functionally graded material (FGM). For the purpose of time-dependent stress analysis in an FGM pressure vessel, material creep behavior and the solutions of the stresses at a time equal to zero (i.e. the initial stress state) are needed. This corresponds to the solution of the problem considering linear elastic behavior of the material. Therefore, using equations of equilibrium, stress–strain and strain–displacement, a differential equation for displacement is obtained and subsequently the initial elastic stresses at a time equal to zero are calculated. Assuming that the Magneto-hygro-thermoelastic creep response of the material is governed by Norton’s law, using the rate form of constitutive differential equation, the displacement rate is obtained and then the stress rates are calculated. Once the stress rates are known, the stresses at any time are calculated iteratively. The analytical solution is obtained for the plane strain condition. The pressure, inner radius and outer radius are considered to be constant and the magnetic field is uniform. Material properties are considered as power law function of the radius of the cylinder and the poisson’s ratio as constant. Following this, profiles are plotted for different values of material exponent for the radial, circumferential and effective stresses as a function of radial direction and time. The in-homogeneity exponent have significant influence on the distributions of the creep stresses. پرونده مقاله

Using the Frobenius series method (FSM), an analytical solution is developed to obtain mechanical stresses of thick spherical pressure vessels made of functionally graded materials (FGMs). The cylinder pressure vessel is subjected to uniform internal pressure. The modulus of elasticity is 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. Primarily, displacements and stresses is obtained as closed-form solutions. Next, the profiles are plotted for different values of inhomogeneity constant along the radial direction. Finally, the problem was solved, using the finite element method (FEM). The obtained results of finite element method were compared with those of the analytical method. The analytical solutions and the solutions carried out through the FEM show good agreement. The values used in this study are arbitrary chosen to demonstrate the effect of inhomogeneity on displacements, and stresses distributions. پرونده مقاله

The present paper provides a semi-analytical solution to obtain the displacements and stresses in a functionally graded material (FGM) rotating thick cylindrical shell with clamped ends under non-uniform pressure. Material properties of cylinder are assumed to change along the axial direction according to a power law form. It is also assumed that the Poisson’s ratio is constant. Given the existence of shear stress in the thick cylindrical shell due to material and pressure changes along the axial direction, the governing equations are obtained based on first-order shear deformation theory (FSDT). These equations are in the form of a set of general differential equations with variable coefficients. Given that the FG cylinder is divided into n homogenous disks, n sets of differential equations with constant coefficients are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. The problem was also solved, using the finite element method (FEM), the results of which were compared with those of the multi-layered method (MLM). Finally, some numerical results are presented to study the effects of applied pressure, non-homogeneity index, and power law index of FGM on the mechanical behavior of the cylindrical shell. پرونده مقاله