The radially nonhomogeneous isotropic spherical shell under a radially varying temperature field

Stampouloglou, I. H.; Theotokoglou, Efstathios E.; Karaoulanis, D.

doi:10.1016/j.apm.2021.01.014

Cited by 4 publications

(5 citation statements)

References 27 publications

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“…: From (45), we obtain that z ¼ AE1:5 is a root for (35). We show that all other roots of Equation ( 35) at ε !…”

Section: Analysis Of the Roots Of The Characteristic Equationmentioning

confidence: 75%

“…Transcendental Equation ( 35) defines a countable set of roots z k , and the corresponding constants C 1k ,C 2k , C 3k , C 4k are proportional to the algebraic complements of the elements of any row of the determinant of system ( 29)- (32). Choosing the algebraic complements of the elements of the first row of the determinant of systems ( 29)- (32) and summing over all roots (35), we obtain solutions of the following form…”

Section: Statement Of Boundary Problem and Construction Of Solutionmentioning

confidence: 99%

“…The general solution of problem ( 15)-( 18) will be a superposition of the solutions corresponding to the different groups of roots of characteristic Equation (35) found above, that is,…”

Section: Construction Of Asymptotic Formulae For Displacements and St...mentioning

confidence: 99%

“…The comparison of the results obtained by the methods of finite elements and spline collocation was carried out. In Stampouloglou et al, 35 the axisymmetric thermoelastic problem was considered for the radially nonhomogeneous spherical shell. In cases, the Poisson's ratio is constant and the exponential and power law varying Young' modulus, the exact analytical solution of the problem was obtained.…”

Section: Introductionmentioning

confidence: 99%

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Investigation of elasticity problem for the radially inhomogeneous transversely isotropic sphere

Akhmedov

Yusubova

2022

Math Methods in App Sciences

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The axisymmetric problem of the theory of elasticity for the radially heterogeneous transverse‐isotopic nonclosed spheres is studied, which does not contain any of the poles 0 and π. The elasticity modules are taken as the linear functions of the radius of the sphere. It is assumed that the lateral surface of the sphere is free from stresses, and in the conical sections, the arbitrary stresses are set that provide equilibrium for the sphere. After consideration of the homogeneous boundary conditions, set on the lateral surfaces of the sphere, the characteristic equation for the spectral parameter is obtained. On the basis of the asymptotic analysis, a classification of the roots of the characteristic equation is made relatively small parameter that characterizes the thickness of the sphere. Corresponding asymptotic solutions are constructed depending on the roots of the characteristic equation. The behavior of the constructed solutions is studied in the internal parts of the sphere, as well as in the neighborhood of the conical sections.

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“…: From (45), we obtain that z ¼ AE1:5 is a root for (35). We show that all other roots of Equation ( 35) at ε !…”

Section: Analysis Of the Roots Of The Characteristic Equationmentioning

confidence: 75%

Section: Statement Of Boundary Problem and Construction Of Solutionmentioning

confidence: 99%

“…The general solution of problem ( 15)-( 18) will be a superposition of the solutions corresponding to the different groups of roots of characteristic Equation (35) found above, that is,…”

Section: Construction Of Asymptotic Formulae For Displacements and St...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Investigation of elasticity problem for the radially inhomogeneous transversely isotropic sphere

Akhmedov

Yusubova

2022

Math Methods in App Sciences

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show abstract

“…The solution is obtained using the matrix similarity transformation and inverse Laplace transform. Stampouloglou et al [16] studied the axisymmetric thermoelastic problem for a radially nonhomogeneous equal thickness spherical shell. They solved the problem under a radially varying temperature field, with axisymmetric geometry and loading.…”

Section: Introductionmentioning

confidence: 99%

Thermal stresses in an orthotropic hollow sphere under thermal shock: a unified generalized thermoelasticity

Soroush,

Soroush

2024

J Eng Math

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This paper deals with the thermoelasticity problem in an orthotropic hollow sphere. A unified governing equation are derived which includes the Classical, Lord-Shulman and Green-Lindsay coupled theories of thermoelasticity. Time-dependent thermal and mechanical boundary conditions are applied to the inner and outer surfaces of the hollow sphere and the problem is solved analytically using the finite Hankel transform. The inner surface of the sphere is subjected to a thermal shock in the form of a prescribed heat flux.Subsequently, the thermal response, radial displacement, as well as radial, tangential, and circumferential stresses of the sphere are determined. The influence of different orthotropic material properties and relaxation time values is investigated and presented graphically. The obtained results demonstrate excellent agreement with the existing literature.

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An analytical method for the thermo-mechanics coupling study of thin-walled spherical shell structure

Zhu

Jiang

Liu

et al. 2021

European Journal of Environmental and Civil Engineering

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The radially nonhomogeneous isotropic spherical shell under a radially varying temperature field

Cited by 4 publications

References 27 publications

Investigation of elasticity problem for the radially inhomogeneous transversely isotropic sphere

Investigation of elasticity problem for the radially inhomogeneous transversely isotropic sphere

Thermal stresses in an orthotropic hollow sphere under thermal shock: a unified generalized thermoelasticity

An analytical method for the thermo-mechanics coupling study of thin-walled spherical shell structure

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