Thermal behavior of functionally graded solid sphere with nonuniform heat generation

Pawar, Siddhesh; Deshmukh, K. C.; Verma, J.

doi:10.1080/01495739.2016.1211928

Cited by 14 publications

(7 citation statements)

References 10 publications

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“…The material properties of sphere are described by power law function which are given by [20] E (r) = Ea(r) n1 (6) α (r) = αa(r) n2 (7) k (r) = ka(r) n3 (8) ρ (r) = ρa(r) n4 (9) q (r) = qa(r) n5 (10) Where, E (r), α (r), k (r), ρ (r), q(r) are elastic modulus, thermal expansion coefficient, thermal conduction coefficient density and heat generation at any radius respectively. Ea, αa, ka, ρa, qa are material properties as described above at inner radius and n 1 , n 2 , n 3 , n 4 , n 5 are material index respectively.…”

Section: Mathematical Formulationmentioning

confidence: 99%

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Exact solution for the thermo-elastic deformation and stress states of FG rotating spherical body

Sahu

Sondhi

Bhowmick

et al. 2020

Journal of the Mechanical Behavior of Materials

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In this paper, a generalized solution for 1-D steady-state mechanical and thermal deformation and stresses in rotating hollow functionally graded spherical body is presented. Spherical shells are treated under mechanical and thermal loads in the form of rotational body force with heat generation. Temperature distribution is assumed to vary along the radial direction due to variable heat generation. General uniform mechanical boundary condition at inner and outer surfaces along with prescribed temperatures at both the ends are assumed as boundary conditions. In the present study, material properties are taken as power function of radius with grading parameter ranging between −2 to 3. Governing differential equation with variable coefficient is developed and solved to find deformation and stresses. The obtained results are verified with benchmark results and are found to be in good agreement. Results show that deformation and stresses decrease with an increase in the value of grading parameter and are less as compared to the homogeneous body.

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Section: Mathematical Formulationmentioning

confidence: 99%

“…The '1-D spherical heat conduction equation with heat generation' under 'steady-state' condition and thermal boundary conditions for FG hollow spherical bodies, are given by [20] 1…”

Section: Temperature Formulationmentioning

confidence: 99%

Exact solution for the thermo-elastic deformation and stress states of FG rotating spherical body

Sahu

Sondhi

Bhowmick

et al. 2020

Journal of the Mechanical Behavior of Materials

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“…Obata and Noda [7] considered steady thermal stresses in a functional graded hollow circular cylinder and hollow sphere and discussed the influence of the inside radius size on stresses. Pawar et al [8] determined thermal stresses in FGM hollow sphere due to non-uniform internal heat generation with radially varying properties by using theory of elasticity and Pawar et al [9] presented the thermoelastic analysis of FGM solid sphere subjected to non-uniform heat source under the constant surface temperature. Yildirim [10] presented a thermo-mechanical analysis of sphere made of non-homogeneous isotropic materials and proposed the closed form formulas for the elastic fields in a simple-power-law graded spheres subjected to steady-state thermal and internal/external pressure loads.…”

Section: Introductionmentioning

confidence: 99%

Thermal Stresses Due to Non-Uniform Internal Heat Generation in Functionally Graded Hollow Cylinder

Rani

Singh

Muwal

2021

International Journal of Applied Mechanics and Engineering

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Thermal stresses of a functionally graded hollow thick cylinder due to non-uniform internal heat generation are studied in this paper. Analytical solutions are obtained with radially varying properties by using the theory of elasticity. Thermal stresses distribution for different values of the powers of the module of elasticity and varying power law index of heat generation are studied. The results have been computed numerically and illustrated graphically.

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“…The material properties of the cylinder are assumed to vary parabolically in the radial direction and results are illustrated for different inhomogeneity constants under uniform temperature field. Pawar et al (2017) examine the thermal response of the FG solid sphere in the vicinity of nonuniform heat generation. The material constituents of metal and ceramic nature are graded along the radial direction with constant Poisson's ratio.…”

Section: Introductionmentioning

confidence: 99%

Thermal stress analysis of functionally graded solid and hollow thick-walled structures with heat generation

Eker

Yarımpabuç

Çelebi

2020

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Purpose This paper aims to present thermal and mechanical stresses in solid and hollow thick-walled cylinders and spheres made of functionally graded materials (FGMs) under the effect of heat generation. Design/methodology/approach Constant internal temperature and convective external conditions in hollow bodies along with internal heat generation with a combination of outer convective conditions in solid bodies are investigated individually. The effect of the heat convection coefficient on solid bodies is additionally discussed. The variation of the FGM properties in the radial direction is adapted to the Mori–Tanaka homogenization schemes, which produces irregular and two-point linear boundary value problems that are numerically solved by the pseudospectral Chebyshev method. Findings It has been shown that the selection of the mixtures of FGMs has to be made correctly to keep the thermal and mechanical loads acting on objects at low levels. Originality/value In this study, both solid and hollow functionally graded cylinders and spheres for different boundary conditions that are as their engineering applications are examined with the proposed method. The results have demonstrated that the pseudospectral Chebyshev method has high accuracy, low calculation costs and ease of application and can be easily adapted to such engineering problems.

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Thermal behavior of functionally graded solid sphere with nonuniform heat generation

Cited by 14 publications

References 10 publications

Exact solution for the thermo-elastic deformation and stress states of FG rotating spherical body

Exact solution for the thermo-elastic deformation and stress states of FG rotating spherical body

Thermal Stresses Due to Non-Uniform Internal Heat Generation in Functionally Graded Hollow Cylinder

Thermal stress analysis of functionally graded solid and hollow thick-walled structures with heat generation

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