Asymmetric Conduction in an Infinite Functionally Graded Cylinder: Two-Dimensional Exact Analytical Solution Under General Boundary Conditions

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Amin Amiri Delouei ◽  
Amin Emamian ◽  
Sajjad Karimnejad ◽  
Hasan Sajjadi ◽  
Dengwei Jing
Keyword(s):  
Temperature Distribution ◽  
Boundary Conditions ◽  
Thermal Stresses ◽  
Exact Analytical Solution ◽  
Full Range ◽  
Functionally Graded ◽  
Graded Materials ◽  
Thermal Boundary Conditions ◽  
Essential Parameter ◽  
General Linear Boundary Conditions

Abstract This paper focuses on using an analytical method to obtain an exact solution for a long cylindrical vessel made of functionally graded materials (FGMs). Heat conduction equations are assumed to be in both radial and circumferential directions. The conduction coefficients are considered as different power-law functions of the radius. The general linear boundary conditions are adopted to make the solution applicable to the full range of problems. The obtained solution is successfully validated. Through solving illustrative test examples, the effects of material constants and boundary conditions on temperature distribution are studied. The obtained formulation can be utilized for tailoring of FGM based on the actual sophisticated thermal boundary conditions in the production process. The current analytical findings can help to manage the temperature distribution in FGMs which is an essential parameter in controlling the thermal stresses.

Assessment on the Thermal Stresses of Concrete Bridge Piers under Solar Radiation

2012 ◽  
Vol 204-208 ◽  
pp. 2045-2050 ◽  
Author(s):  
Pei Song Gong ◽  
Bo Chen ◽  
Chun Fang Song ◽  
Xiu Li Li
Keyword(s):  
Temperature Distribution ◽  
Boundary Conditions ◽  
Thermal Stresses ◽  
Numerical Models ◽  
Bridge Pier ◽  
Concrete Bridge ◽  
Time Varying ◽  
Thermal Boundary Conditions ◽  
Infrared Imager ◽  
Structural Temperature

The time-varying thermal stresses of a concrete pier are actively studied in this study with the aiding of the commercial package ANSYS. Thermal boundary conditions are utilized to obtain the temperature distribution of the concrete bridge pier. The surface temperature of the pier is measured by using a thermal infrared imager at different time instants. The different boundary conditions are applied to determine the structural temperature distribution and compute the thermal deformation. The made observations demonstrate that the horizontal deformation is much larger than that in vertical deformation due to the influence of the constraints on the top and bottom sides of the pier. The thermal stresses of the example bridge pier are not very large except for the local areas on top of the piers. It is seen that the numerical models can successfully predict the structural time-varying temperature effects

Effects of structural thermal boundary conditions on hypersonic aerothermoelasticity of all-movable control surface

2018 ◽  
Vol 233 (7) ◽  
pp. 2673-2689 ◽  
Author(s):  
Kun Ye ◽  
ZhengYin Ye ◽  
XianZong Meng ◽  
Zhan Qu
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Boundary Conditions ◽  
Thermal Stresses ◽  
Stokes Equations ◽  
Thermal Environment ◽  
The Body ◽  
Control Surface ◽  
Aerodynamic Heating ◽  
Thermal Boundary Conditions

Structural thermal boundary conditions are usually simplified in the aerothermoelastic analysis. However, it will influence the heat transfer, the temperature distribution, and the structure stiffness, which have effects on the accurate prediction of the aerothermoelastic characteristics. In this study, an aerothermoelastic framework for hypersonic vehicles is developed, and the effects of structural thermal boundary conditions on aerothermoelasticity of all-movable control surface are investigated. The Reynold’s averaged Navier–Stokes equations are solved by computational fluid dynamics method to obtain the thermal environment. The transient heat transfer, the thermal stress, and the structure mode are analyzed by using finite element method. Finally, the local piston theory is used to calculate the unsteady aerodynamic force, and aeroelastic characteristics are analyzed in the state space. Aerothermoelastic characteristics of three different structural thermal boundaries are investigated in detail, including aerodynamic heating only on control surface; aerodynamic heating on both the control surface and the shaft; and aerodynamic heating on the control surface, the shaft, and the body. The results show that the heat transfer process, the temperature distribution, the thermal stresses, and the natural frequencies of the structure are influenced significantly by structural thermal boundary conditions especially in the shaft. Furthermore, the aerothermoelastic stability margin is affected ultimately.

scholarly journals Three-Dimensional Finite Element Modeling of Thermomechanical Problems in Functionally Graded Hydroxyapatite/Titanium Plate

2014 ◽  
Vol 2014 ◽  
pp. 1-20 ◽  
Author(s):  
S. N. S. Jamaludin ◽  
S. Basri ◽  
Ahmad Hussain ◽  
Dheya Shujaa Al-Othmany ◽  
F. Mustapha ◽  
...  
Keyword(s):  
Thermal Stresses ◽  
Three Dimensional ◽  
Metallic Phase ◽  
Functionally Graded ◽  
Thermomechanical Model ◽  
Graded Materials ◽  
Ceramic Phase ◽  
Fg Plates ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

The composition of hydroxyapatite (HA) as the ceramic phase and titanium (Ti) as the metallic phase in HA/Ti functionally graded materials (FGMs) shows an excellent combination of high biocompatibility and high mechanical properties in a structure. Because the gradation of these properties is one of the factors that affects the response of the functionally graded (FG) plates, this paper is presented to show the domination of the grading parameter on the displacement and stress distribution of the plates. A three-dimensional (3D) thermomechanical model of a 20-node brick quadratic element is used in the simulation of the thermoelastic behaviors of HA/Ti FG plates subjected to constant and functional thermal, mechanical, and thermomechanical loadings. The convergence properties of the present results are examined thoroughly in order to assess the accuracy of the theory applied and to compare them with the established research results. Instead of the grading parameter, this study reveals that the loading field distribution can be another factor that reflects the thermoelastic properties of the HA/Ti FG plates. The FG structure is found to be able to withstand the thermal stresses while preserving the high toughness properties and thus shows its ability to operate at high temperature.

TRANSIENT HEAT CONDUCTION IN FUNCTIONALLY GRADED MATERIALS

2007 ◽  
Vol 04 (04) ◽  
pp. 603-619 ◽  
Author(s):  
S. M. HAMZA-CHERIF ◽  
A. HOUMAT ◽  
A. HADJOUI
Keyword(s):  
Heat Conduction ◽  
Temperature Distribution ◽  
Functionally Graded Materials ◽  
Degrees Of Freedom ◽  
Functionally Graded ◽  
P Element ◽  
Transient Temperature ◽  
Test Problems ◽  
Shape Functions ◽  
Graded Materials

The h-p version of the finite element method (FEM) is considered to determine the transient temperature distribution in functionally graded materials (FGM). The h-p version may be regarded as the marriage of conventional h-version and p-version. The graded Fourier p-element is used to set up the two-dimensional heat conduction equations. The temperature is formulated in terms of linear shape functions used generally in FEM plus a variable number of trigonometric shape functions representing the internal degrees of freedom (DOF). In the graded Fourier p-element, the function of the thermal conductivity is computed exactly within the conductance matrix and thus overcomes the computational errors caused by the space discretization introduced by the FEM. Explicit and easily programmed trigonometric enriched capacitance, conductance matrices and heat load vectors are derived for plates and cylinders by using symbolic computation. The convergence properties of the h-p version proposed and the results of the numbers of test problems are in good agreement with the analytical solutions. Also, the effect of the non-homogeneity of the FGM on the temperature distribution is considered.

An Analysis of Thermo-Mechanical Behavior in a Multilayer Composite Pipe Under Temperature Variation

2010 ◽  
Author(s):  
Wei Yang ◽  
Jyhwen Wang
Keyword(s):  
Finite Element ◽  
Thermal Stress ◽  
Analytical Solution ◽  
Mechanical Behavior ◽  
Temperature Change ◽  
Thermal Stresses ◽  
Element Model ◽  
Functionally Graded ◽  
Element Analysis ◽  
Graded Materials

A generalized analytical solution of mechanical and thermal induced stresses in a multi-layer composite cylinder is presented. Based on the compatibility condition at the interfaces, an explicit solution of mechanical stress due to inner and outer surface pressures and thermal stress due to temperature change is derived. A finite element model is also developed to provide the comparison with the analytical solution. It was found that the analytical solutions are in good agreement with finite element analysis result. The analytical solution shows the non-linear dependency of thermal stress on the diameters, thicknesses and the material properties of the layers. It is also shown that the radial and circumferential thermal stresses depend linearly on the coefficients of thermal expansion of the materials and the temperature change. As demonstrated, this solution can also be applied to analyze the thermo-mechanical behavior of pipes coated with functionally graded materials.

Bi-Directional Functionally Graded Nanotubes: Fluid Conveying Dynamics

2018 ◽  
Vol 10 (04) ◽  
pp. 1850041 ◽  
Author(s):  
Ye Tang ◽  
Tianzhi Yang
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Differential Quadrature Method ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Graded Materials ◽  
Critical Flow Velocity ◽  
Dynamic Behaviors ◽  
Fundamental Frequencies ◽  
Material Gradation

In the paper, a novel model of fluid-conveying nanotubes made of bi-directional functionally graded materials is presented for investigating the dynamic behaviors and stability. For the first time, the material properties of the nanotubes along both radical and axial directions are under consideration. Based on Euler–Bernoulli beam and Eringen’s nonlocal elasticity theories, the governing equation of the nanotubes and associated boundary conditions are developed using Hamilton’s principle. Differential quadrature method (DQM) is applied for discretizing the equation to determine the numerical solutions of the nanotubes with different boundary conditions. Numerical examples are presented to examine the effects of the material gradation, nonlocal parameter, and mode order on the dynamics and stability. It is shown that the two-directional materials distribution can significantly change the critical flow velocity, fundamental frequencies and stability. Comparing with traditional one-directional distribution, such 2D is more flexible to tune overall dynamic behaviors, this may provide new avenues for smart pipes.

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