Analytical Solution of Thermal Stresses in a Functionally Graded Solid Cylinder within Parabolic Continuous Grading

2013 ◽  
Vol 307 ◽  
pp. 364-367 ◽  
Author(s):  
Ali Ozturk ◽  
Müfit Gülgeç
Keyword(s):  
Thermal Expansion ◽  
Analytical Solution ◽  
Material Properties ◽  
Thermal Conduction ◽  
Thermal Stresses ◽  
Elasticity Modulus ◽  
Functionally Graded ◽  
Solid Cylinder ◽  
Graded Materials ◽  
Parabolic Form

This paper presents analytical solutions of the thermal stresses in a functionally graded solid cylinder with fixed ends in elastic region. These thermal stresses are due to the uniform heat generation inside the cylinder. Material properties of the functionally graded (FG) cylinder vary radially according to a parabolic form. The material properties are assumed to be independent of the temperature which are yield strength, elasticity modulus, thermal conduction coefficient, thermal expansion coefficient and Poisson’s ratio. The solutions for the thermal stresses are valid for both homogeneous and functionally graded materials.

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.

Characterization of the Tungsten-Steel Functionally Graded Cylinder in Elastic Region

2017 ◽  
Vol 263 ◽  
pp. 67-71
Author(s):  
Ali Ozturk
Keyword(s):  
Stress Function ◽  
Thermal Stresses ◽  
Coefficient Of Thermal Expansion ◽  
Functionally Graded ◽  
Elastic Region ◽  
Airy Stress Function ◽  
Solid Cylinder ◽  
Average Value ◽  
Parabolic Form ◽  
Tungsten Steel

This paper presents how to derive Airy stress function to obtain the thermal stresses in a tungsten-steel functionally graded solid cylinder with fixed ends in elastic region. Once Airy stress function is derived, the thermal stresses can be found due to the related equations. There is uniform heat generation inside the tungsten-steel functionally graded solid cylinder. Material properties of the functionally graded cylinder (FGC) are assumed to vary radially according to a parabolic form and assumed to be independent of the temperature. These properties are yield strength, modulus of elasticity, coefficient of thermal conduction and coefficient of thermal expansion (CTE). Poisson’s ratio is assumed to be constant as an average value between tungsten’s and steel’s. Airy stress function is derived in terms of these properties to characterize the FGC entirely.

Free Vibration Analysis of FGM Plates under Initial Thermal Stresses

2013 ◽  
Vol 682 ◽  
pp. 49-56 ◽  
Author(s):  
A. Mahi ◽  
E.A. Adda-Bedia ◽  
A. Benkhedda
Keyword(s):  
Free Vibration ◽  
Material Properties ◽  
Thermal Stresses ◽  
Plate Theory ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Energy Functional ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Graded Materials

Functionally graded materials (FGMs) are a new kind of composite materials which have a smooth variation of material properties along one or more directions. At each interface, the material is chosen according to specific applications and environment loadings. This paper presents some solutions to study the free vibration of FGM plates made of ceramic and metal. The formulation used is based on Reddys higher order shear deformation plate theory. Material properties are taken to be temperature-dependent, and vary continuously through the thickness direction according to a power law distribution (P-FGM). The plate is assumed to be initially stressed by temperature rise through the thickness. The energy functional of the system is obtained by using energy principles. Free vibration frequencies are then obtained by using a set of characteristic orthogonal polynomials and by applying Ritz method.

Thermomechanical Analysis in FG Rotating Hollow Disk

2011 ◽  
Vol 110-116 ◽  
pp. 148-154 ◽  
Author(s):  
A. R. Khorshidvand ◽  
M. Jabbari
Keyword(s):  
Heat Conduction ◽  
Material Properties ◽  
Radial Direction ◽  
Thermal Stresses ◽  
Energy Equation ◽  
Elliptic Cylinder ◽  
Thermomechanical Analysis ◽  
Functionally Graded ◽  
Exponential Functions ◽  
Graded Materials

In this paper, mechanical and thermal stresses of rotating hollow disks composed of functionally graded materials (FGMs) is presented. The material properties for FG are expressed as nonlinear exponential functions through the radius of disk and Poisson’s ratio is taken to be constant. The temperature distribution is derived from first law thermodynamics by solving energy equation, general thermal and mechanical boundary conditions are assumed on the inside and outside surfaces of the disk. Heat conduction and Navier equations of a FGM disk are expressed in elliptic cylinder coordinates system and solved analytically. The results are shown for displacement and stresses components along the radial direction.

scholarly journals Thermoelastic Analysis of Functionally Graded Hollow Circular Disc

2015 ◽  
Vol 62 (1) ◽  
pp. 5-18 ◽  
Author(s):  
Dávid Gönczi ◽  
Istvàn Ecsedi
Keyword(s):  
Analytical Solution ◽  
Material Properties ◽  
Thermal Stresses ◽  
Poisson Ratio ◽  
Functionally Graded ◽  
Circular Disc ◽  
Radial Coordinate ◽  
Thermal Loads ◽  
Power Functions ◽  
Smooth Functions

Abstract A thermoelastic boundary value problem of a hollow circular disc made of functionally graded materials with arbitrary gradient is analysed. The steady-state temperature distribution is assumed to be the function of the radial coordinate with prescribed temperature at the inner and outer cylindrical boundary surfaces. The material properties are assumed to be arbitrary smooth functions of the radial coordinate. A coupled system of ordinary differential equations containing the radial displacement and stress function is derived and used to get the distribution of thermal stresses and radial displacements caused by axisymmetric mechanical and thermal loads. General analytical solutions of functionally graded disc with thermal loads are not available. The results obtained by the presented numerical method are verified by an analytical solution. The considered analytical solution is valid if the material properties, except the Poisson ratio, are expressed as power functions of the radial coordinate.

Analytical and numerical investigation of the free vibration of functionally graded materials sandwich beams

2021 ◽  
Vol 2 (110) ◽  
pp. 72-85
Author(s):  
S.H. Bakhy ◽  
M. Al-Waily ◽  
M.A. Al-Shammari
Keyword(s):  
Analytical Solution ◽  
Free Vibration ◽  
Functionally Graded Materials ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Functionally Graded ◽  
Gradient Index ◽  
Sandwich Beams ◽  
Graded Materials ◽  
The Impact

Purpose: In this study, the free vibration analysis of functionally graded materials (FGMs) sandwich beams having different core metals and thicknesses is considered. The variation of material through the thickness of functionally graded beams follows the power-law distribution. The displacement field is based on the classical beam theory. The wide applications of functionally graded materials (FGMs) sandwich structures in automotive, marine construction, transportation, and aerospace industries have attracted much attention, because of its excellent bending rigidity, low specific weight, and distinguished vibration characteristics. Design/methodology/approach: A mathematical formulation for a sandwich beam comprised of FG core with two layers of ceramic and metal, while the face sheets are made of homogenous material has been derived based on the Euler–Bernoulli beam theory. Findings: The main objective of this work is to obtain the natural frequencies of the FG sandwich beam considering different parameters. Research limitations/implications: The important parameters are the gradient index, slenderness ratio, core metal type, and end support conditions. The finite element analysis (FEA), combined with commercial Ansys software 2021 R1, is used to verify the accuracy of the obtained analytical solution results. Practical implications: It was found that the natural frequency parameters, the mode shapes, and the dynamic response are considerably affected by the index of volume fraction, the ratio as well as face FGM core constituents. Finally, the beam thickness was dividing into frequent numbers of layers to examine the impact of many layers' effect on the obtained results. Originality/value: It is concluded, that the increase in the number of layers prompts an increment within the frequency parameter results' accuracy for the selected models. Numerical results are compared to those obtained from the analytical solution. It is found that the dimensionless fundamental frequency decreases as the material gradient index increases, and there is a good agreement between two solutions with a maximum error percentage of no more than 5%.

Designing Optimal Volume Fractions For Functionally Graded Materials With Temperature-Dependent Material Properties

2006 ◽  
Vol 74 (5) ◽  
pp. 861-874 ◽  
Author(s):  
Florin Bobaru
Keyword(s):  
Functionally Graded Materials ◽  
Material Properties ◽  
Volume Fraction ◽  
Effective Properties ◽  
Functionally Graded ◽  
Dominant Factor ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Critical Stresses ◽  
Non Linear

We present a numerical approach for material optimization of metal-ceramic functionally graded materials (FGMs) with temperature-dependent material properties. We solve the non-linear heterogeneous thermoelasticity equations in 2D under plane strain conditions and consider examples in which the material composition varies along the radial direction of a hollow cylinder under thermomechanical loading. A space of shape-preserving splines is used to search for the optimal volume fraction function which minimizes stresses or minimizes mass under stress constraints. The control points (design variables) that define the volume fraction spline function are independent of the grid used in the numerical solution of the thermoelastic problem. We introduce new temperature-dependent objective functions and constraints. The rule of mixture and the modified Mori-Tanaka with the fuzzy inference scheme are used to compute effective properties for the material mixtures. The different micromechanics models lead to optimal solutions that are similar qualitatively. To compute the temperature-dependent critical stresses for the mixture, we use, for lack of experimental data, the rule-of-mixture. When a scalar stress measure is minimized, we obtain optimal volume fraction functions that feature multiple graded regions alternating with non-graded layers, or even non-monotonic profiles. The dominant factor for the existence of such local minimizers is the non-linear dependence of the critical stresses of the ceramic component on temperature. These results show that, in certain cases, using power-law type functions to represent the material gradation in FGMs is too restrictive.

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.

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