Nonlinear Thermal Buckling Analysis of FGM Shallow Arches Under Linear Temperature Gradient

2014 ◽  
Author(s):  
H. Asgari ◽  
M. R. Eslami
Keyword(s):  
Temperature Gradient ◽  
Power Law ◽  
Material Properties ◽  
Thermal Buckling ◽  
Functionally Graded ◽  
Bottom Surface ◽  
Linear Temperature ◽  
Shallow Arches ◽  
Linear Temperature Gradient ◽  
Non Linear

In this study non-linear thermal buckling of circular shallow arches made of functionally graded materials subjected to a linear temperature gradient is investigated. For this purpose, a functionally graded circular shallow arch is considered that its strain-displacement relation follows the Donnells nonlinear shallow shell theory. The material properties are varied smoothly through the arch thickness according to the power law distribution of the volume fraction of constituent materials. Also, material properties are considered temperature-dependent. The classical single layer theory assumptions that are reasonable for slender arches are implemented. To investigate the large deformations of such arch, the von-Karman type geometrical nonlinearity is utilized that is suitable for moderately large class of rotations. The virtual displacement principle and calculus of variation are employed to derive the governing equilibrium equations and complete set of boundary conditions of the FGM arch. The adjacent equilibrium criterion is employed for the stability analysis of the FGM arch. An analytical approach is accomplished and a closed-forms solution for thermal bifurcation points of the FGM shallow arches is presented. Also critical bifurcation loads corresponding to the critical temperatures with the presence of non-linear pre-buckling deformations is obtained. Illustrative results examine the effect of various involved parameters such as power law index, opening angle, geometric parameter (or otherwise length to thickness ratio). Obtained numerical results represent that, in most cases, thermal bifurcation for the FGM arches occurs in the high temperatures and the critical buckling temperatures are approximately high even for slender FGM arches. Also effective of ceramic or metal rich area at the bottom surface of the FGM arch is investigated and results are presented for both cases and are compared together. Varieties between this two cases due to contrast between material and structural stretching-bending coupling effect. Results presented illustrative the ceramic rich area at the bottom surface cause the higher critical buckling temperatures for the FGM arches.

scholarly journals Functionally Graded Panels: A Review

2020 ◽  
pp. 36-43
Author(s):  
C. Pany Sreeju Nair S B
Keyword(s):  
Free Vibration ◽  
Power Law ◽  
Material Properties ◽  
Structural Model ◽  
Constitutive Relations ◽  
Functionally Graded ◽  
Bottom Surface ◽  
Power Law Distribution ◽  
Literature Study ◽  
Static And Dynamic Analysis

Functionally gradedmaterials (FGMs) are not homogeneous materials. It consists of different(two or more) materials, engineered to have a continuously varying spatial composition profile. FGM is the one that can solve practical problems arising from the production and application of a new type of composite material. This paper describes the overview of FGM basic concepts, classification, properties, and its modeling which may focus on the static and dynamic analysis of functionally graded panels. The effective material properties of functionally graded materials for the panel are graded in the thickness direction from the bottom surface to the top surface according to the power-law distribution of volume fractions of the constituents. The use of structures like beams, plates, and shells, which are made from functionally graded (FG) materials, is increasing because of the smooth variation of material properties along with preferred directions. This variation gives continuous stress distribution in the FG structures. Therefore, an FGM can be effectively used in avoiding corrosion, fatigue, fracture, and stress corrosion cracking. The paper covers the literature study on static, buckling and free vibration, thermo-mechanical analysis of FGM panel. From this literature study it is found that, analysis of these problems is made using the constitutive relations and governing equations associated with the classical laminated theory structural model, the FSDT model, the HSDT model,Reissner and Sander theory,differential quadrature, finite element method and closed form solutions. Results are availableon different geometrical dimensional ratios variations, power-law index value n variationsand simply supported,clamped, free edges boundary conditionswith its combinations for FG panels. Lesser literatures are available for different edge boundary conditions such as SCSC, CSCS,SSSC, SFSF, SSSF, SCSF on curved panelfor free vibration, buckling and thermo-structural analysis.

A LINEAR THERMOELASTIC BUCKLING BEHAVIOR OF FUNCTIONALLY GRADED HEMISPHERICAL SHELL WITH A CUT-OUT AT APEX IN THERMAL ENVIRONMENT

2005 ◽  
Vol 05 (02) ◽  
pp. 185-215 ◽  
Author(s):  
RAJESH K. BHANGALE ◽  
N. GANESAN
Keyword(s):  
High Temperature ◽  
Power Law ◽  
Material Properties ◽  
Thermal Buckling ◽  
Functionally Graded ◽  
Fourier Series Expansion ◽  
Element Formulation ◽  
Hemispherical Shell ◽  
Buckling Behavior ◽  
Hemispherical Shells

In this paper, a finite element formulation based on first-order shear deformation theory (FSDT) is used to study the thermal buckling behavior of functionally graded material (FGM) hemispherical shells with a cut-out at apex in a high temperature environment. A Fourier series expansion for the displacement variable in the circumferential direction is used to model the FGM hemispherical shell. The material properties of FGM hemispherical shells are functionally graded in the thickness direction according to a volume fraction power law distribution. Temperature-dependent material properties are considered to carry out a linear thermal buckling analysis. The hemispherical shell is assumed to be clamped–clamped and has a high temperature specified on the inner surface while the outer surface is at ambient temperature. The one-dimensional heat conduction equation is applied along the thickness of the shell to determine the temperature distribution and thereby material properties. Converged critical buckling temperatures are computed for two cases of thermal loads, namely, under uniform temperature rise and temperature gradient across the thickness. Numerical studies include the influence of, power law index, base to radius ratios, and different cut-out angles at the apex on the magnitude of thermal buckling temperature.

Thermal Buckling Behaviour of Functionally Graded Plates

2016 ◽  
Vol 857 ◽  
pp. 279-284
Author(s):  
Alex Ancy ◽  
U. Parvathy
Keyword(s):  
Aspect Ratio ◽  
Power Law ◽  
Temperature Rise ◽  
Material Properties ◽  
Thermal Buckling ◽  
Functionally Graded ◽  
Thickness Ratio ◽  
Functionally Graded Plates ◽  
Continuous Change ◽  
Ansys Software

Functionally Graded Materials (FGM) are those materials which have continuous variation of material properties from metal phase to ceramic phase. Due to the continuous change in material properties of FGMs, the stress singularity at the interface between the two different materials is eliminated and thus the bonding strength is enhanced. They are widely used in high temperature environment such as nuclear reactors and rocket heat shields. The material property of FGM plate varies along the thickness direction and the variation is idealised by different mathematical idealisation techniques. This paper deals with the buckling behaviour of clamped PFGM plate under uniform temperature field. Thermal buckling behaviour of FGM plate has been obtained numerically through ANSYS software. The convergence study of the results is optimized by changing the mesh size. The critical buckling temperature rise obtained for functionally graded plates using ANSYS software are compared with the available literature. The effect of different parameters such as power-law index, thickness ratio, and aspect ratio on critical buckling temperature rise for temperature independent and dependent material properties of each constituent is also discussed. It is found that the critical buckling temperature rise decreases with the increase in power-law indices and thickness ratio and increases with increase in aspect ratio.

scholarly journals Microfluidic Platform for Analyzing the Thermotaxis of C. elegans in a Linear Temperature Gradient

2017 ◽  
Vol 33 (12) ◽  
pp. 1435-1440 ◽  
Author(s):  
Sunhee YOON ◽  
Hailing PIAO ◽  
Tae-Joon JEON ◽  
Sun Min KIM
Keyword(s):  
Temperature Gradient ◽  
Linear Temperature ◽  
Microfluidic Platform ◽  
C Elegans ◽  
Linear Temperature Gradient

Effect of Temperature Gradient on the Mechanical Buckling Resistance of FGM Shallow Arches

2014 ◽  
Author(s):  
M. Bateni ◽  
M. R. Eslami
Keyword(s):  
Temperature Gradient ◽  
Thermal Environment ◽  
Mechanical Load ◽  
Functionally Graded ◽  
Effect Of Temperature ◽  
Power Law Distribution ◽  
Concentrated Load ◽  
Shallow Arches ◽  
Buckling Resistance ◽  
Graded Material

This work presents a closed form investigation on the effect of temperature gradient on the buckling resistance of functionally graded material (FGM) shallow arches. The constituents are assumed to vary smoothly through the thickness of the arch according to the power law distribution and they are assumed to be temperature dependent. The arches subjected to the both uniform distributed radial load and central concentrated load and both boundary supports are supposed to be pinned. The temperature field is approximated by one-dimensional linear gradient through the thickness of the arch and the displacement field approximated by classical arches model. Also, Donnell type kinematics is utilized to extract the suitable strain-displacement relations for shallow arches. Adjacent equilibrium criterion is used to buckling analysis, and, critical bifurcation load is obtain in the complete presence of pre-buckling deformations. Results discloses the usefulness of using the FGM shallow arches in thermal environment because the temperature gradient enhances the buckling resistance of these structures when they are subjected to a lateral mechanical load.

An Analytical Solution Countercurrent Heat Transfer Between Parallel Vessels With a Linear Axial Temperature Gradient

1988 ◽  
Vol 110 (3) ◽  
pp. 254-256 ◽  
Author(s):  
E. H. Wissler
Keyword(s):  
Heat Transfer ◽  
Temperature Field ◽  
Heat Exchange ◽  
Temperature Gradient ◽  
Infinite Medium ◽  
Linear Temperature ◽  
Linear Temperature Gradient ◽  
Axial Temperature ◽  
Mixed Mean ◽  
The Difference

Presented in this paper is a solution for countercurrent heat exchange between two parallel vessels embedded in an infinite medium with a linear temperature gradient along the axes of the vessels. The velocity profile within the vessel is assumed to be parabolic. This solution describes the temperature field within the vessels, as well as in the tissue, and establishes that the intravessel temperature is not uniform, as is generally assumed to be the case. An explicit expression for the intervessel thermal resistance based on the difference between cup-mixed mean temperatures is derived.

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.

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