Sharif Digital Repository

An analytical thermoelasticity solution for hollow finite-length cylinders made of functionally graded materials exposed to thermal loads, internal pressure and axial loadings is presented. For this purpose, the governing differential equations of equilibrium are obtained using the principle of minimum total potential energy. A first-order shear deformation shell theory, which accounts for the transverse shear strains and rotations, is considered for expressing displacement field. The governing differential equations are reduced to a set of linear algebraic equations using Fourier expansion series of the displacement field components in the axial coordinate. Subsequently, solution of the... 

In this paper, strain gradient thermo-elasticity formulation for axisymmetric Functionally Graded (FG) thick-walled cylinders is presented. For this purpose, the elastic strain energy density function is considered to be a function of gradient of strain tensor in addition to the strain tensor. The material properties are assumed to vary according to a power law in radial direction. Using the constitutive equations and equation of equilibrium in the cylindrical coordinates, a fourth order non-homogenous governing equation for thermo-elastic analysis of thick-walled FG cylinders subjected to thermal and mechanical loadings is obtained and solved numerically. Results show that the intrinsic... 

Special superelements are often used to improve the computational efficiency and improve accuracy of finite element modeling. Structures with tapered and spherical geometry exist in many engineering problems. In this work, special tapered and spherical superelements are presented that can be used for modeling of tapered and spherical bodies in thermo mechanical analyses with computational efficiency. The performance of these superelements under thermal and structural loads is demonstrated by presenting several examples and comparing the results with those from conventional 3D brick elements, which shows high accuracy at reduced computational cost  

A variable kinematic 1D finite element (FE) method is presented for 3D thermoelastic analysis of rotating disks with variable thickness. The principle of minimum potential energy is used to derive general governing equations of the disks subjected to body forces, surface forces, concentrated forces, and thermal loads. To solve the equations, the 1D Carrera unified formulation (CUF), which enables to go beyond the kinematic assumptions of classical beam theories, is employed. Based on the 1D CUF, the disk is considered as a beam, which can be discretized into a finite number of 1D elements along its axis. The displacement field over the beam’s cross section is approximated by Lagrange... 

The aero-thermo-elastic stability of layered cylindrical shells with viscoelstic cores is investigated. The Donnell's shell theory for the outer layers and the first order shear deformation theory for the viscoelastic layer are employed in conjunction with the von Karman-Donnell kinematic nonlinearity to construct the model. The pre-stresses and pre-deformations arisen from the temperature rise and static aerodynamic pressure are first determined by solving the nonlinear thermo-elastic equilibrium equations using by an exact analytical method. The results are then used in the linear aeroelastic stability equations and analyzed with the Galerkin's procedure to determine the supersonic flutter... 

An innovative 1D finite element (FE) approach is developed to analyze the 3D static, transient, and dynamic problems in the coupled and uncoupled thermoelasticity for the nonhomogeneous anisotropic materials. The Galerkin method is directly applied to the governing equations to obtain a weak formulation of the thermoelasticity problems with arbitrary loads and boundary conditions. To surmount the restrictions of the classical beam theories, a 1D FE procedure is proposed in the context of the Carrera Unified Formulation (CUF). Since coupled thermoelastic analyses are computationally demanding, the proposed 1D FE approach can be used as a powerful means to simulate the generalized coupled... 

This article aims to evaluate the high-fidelity one-dimensional finite elements that have been proposed in the companion article (Part 1). Simple structural configurations that are subjected to different loading and boundary conditions have been considered to demonstrate the generality of the proposed approach. Static, quasi-static, and dynamic analyses of the coupled and uncoupled thermoelasticity have been performed. The kinematics of the beam elements have been obtained using bidimensional Lagrangian expansions with different polynomial orders. In particular, bilinear, biquadratic, and bicubic expansions have been adopted to approximate both displacements and temperature change field.... 

A finite element formulation is derived for the thermoelastic analysis of functionally graded (FG) plates and shells. The power-law distribution model is assumed for the composition of the constituent materials in the thickness direction. The procedure adopted to derive the finite element formulation contains the analytical through-the-thickness integration inherently. Such formulation accounts for the large gradient of the material properties of FG plates and shells through the thickness without using the Gauss points in the thickness direction. The explicit through-the-thickness integration becomes possible due to the proper decomposition of the material properties into the product of a... 

In this paper, strain gradient thermo-elasticity formulation for Functionally Graded (FG) thick-walled cylinders is presented. Elastic strain energy density function is considered to be a function of gradient of strain tensor in addition to the strain tensor. The material properties are assumed to vary according to power law in radial direction. Using the constitutive equations and equation of equilibrium in the cylindrical coordinates, fourth order non-homogenous governing equation for thermo-elastic analysis of thick-walled FG cylinders subjected to thermal and mechanical loadings is obtained and solved numerically. Results show that the intrinsic length parameter affects the stress... 

A thermo-elastic analysis coupled with a phase change model is employed to evaluate thermal stresses as well as progress of austenite decomposition after hot strip rolling operations. The thermo-mechanical finite element analysis is utilized to assess the distributions of temperature and thermal stresses during cooling while at the same time, a model based on the additivity rule is used to determine the rate of austenite to ferrite decomposition. The proposed model is applicable to multi-pass rolling schedules while the effects of different process parameters including the rolling speed and cooling configuration of the run-out table can be taken into account. In order to verify the... 

In this paper effects of material properties estimations, used for particulate reinforced composites, on the thermo-mechanical response of functionally graded sphere and cylinder are presented. A numerical solution for an arbitrary material gradation is obtained for each geometry independently. With this assumption, the governing partial differential equations are reduced to an ordinary differential equation in each geometry. The thermo-elastic solution for hollow sphere is derived using spherical symmetry. However, plane strain and axial symmetry are assumed for solving hollow cylinder. In the numerical method, radial domain is divided into some finite sub-domains and material properties... 

Aero-thermoelastic analysis of a simply supported functionally graded truncated conical shell subjected to supersonic air flow is performed to predict the flutter boundaries. The temperature-dependent properties of the FG shell are assumed to be graded through the thickness according to a simple rule of mixture and power-law function of volume fractions of material constituents. Through the thickness steady-state heat conduction is considered for thermal analysis. To perform the stability analysis, the general nonlinear equations of motion are first derived using the classical Love's shell theory and the von Karman-Donnell-type of kinematic nonlinearity together with the linearized...