Thermoelastic strain and stress fields due to a spherical inclusion in an elastic half-space

Singh, Kuldip; Muwal, Renu

doi:10.15632/jtam-pl.55.4.1369

Cited by 3 publications

(3 citation statements)

References 22 publications

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“…Equations (33)(34)(35) is a linear equations system with A ni (s), c n as an unidentified parameter. When we solve such equations, we have a perfect solution to the transform domain issue.…”

Section: Laplace Transform Domain Solutionmentioning

confidence: 99%

Untitled

2023

Adv. Math., Sci. J.

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In the present article, we implement the fractional thermoelasticity theory to a 2D issue for a sphere whose surface is free from traction, subject to a provided axisymmetric temperature distribution of heat. The medium is supposed to be quiescent initially. A direct method is used to get a solution and the Laplace transform technique is used. Mathematical models for copper material are designed as a particular instance. Numerical results are computed with help of Mathcad software and graphically represented and the fractional-order parameter effect has been explained. Nomenclature: t Time T Absolute temperature ρ Density λ, µ Lamé's constants e Cubical dilation = div u γ = (3λ + 2µ)α t σ ij Stress tensor components

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Section: Laplace Transform Domain Solutionmentioning

confidence: 99%

Untitled

2023

Adv. Math., Sci. J.

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Section: Laplace Transform Domain Solutionmentioning

confidence: 99%

On Graded S-Primary Submodules of Graded Modules Over Graded Commutative Rings

Al-Zoubi¹,

Ababneh²

2022

Adv. Math., Sci. J.

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Let $G$ be a group, $R$ be a $G$-graded commutative ring with identity, $M$ be a graded $R$-module and $S\subseteq h(R)$ be a multiplicatively closed subset of $R$. In this paper, a new concept of graded $S$-primary submodules of $M$ is introduced as a generalization of graded Primary submodules as well as a generalization of graded $S$-prime submodules of $M$. Also, some properties of this class are investigated.

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“…Sharma et al [13] presented transient wave analysis in functionally graded thermoelastic spherical cavity in radial direction using series solution. Singh and Muwal [14] presented the analytical results for thermoelastic stress and stain fields due to spherical inclusion for exterior and interior points. Sharma et al [15] studied generalized thermoelastic hollow cylinder analytically with the effect of 3-phase-lag model and analyzed the results graphically.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Free Vibrations in Homogeneous Isotropic Rigidly Fixed Thermoelastic Circumferential Spherical Curved Plates

Sharma¹,

Sharma

2022

Trends Sci

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The 1st and 2nd class vibrations of rigidly fixed thermoelastic spherical curved plates have been presented in this article. After mathematical modeling, the obtained equations have been solved by applying normal mode analysis. The uncoupled equation has been considered as 1st class vibrations named toroidal vibrations, remains independent of temperature variations. The coupled system of equations which is considered as 2nd class vibrations named spheroidal vibrations. The series solution of matrix Fröbenius method has been applied to coupled system of ordinary differential equations to obtain potentials and temperature. Fixed point iteration numerical technique has been applied to analytical results with the assistance of MATLAB software tools. Computational techniques have been applied to analytical results and numerically generated data has been represented graphically for frequencies, dissipation factor, displacements and temperature. HIGHLIGHTS The 1st and 2nd class vibrations of rigidly fixed thermoelastic spherical curved plates have been presented in this article The uncoupled equation has been considered as 1st class vibrations named toroidal vibrations, remains independent of temperature variations The coupled system of equations which is considered as 2nd class vibrations named spheroidal vibrations The series solution of matrix Fröbenius method has been applied to couple system of ordinary differential equations to obtain potentials and temperature Computational techniques have been applied to analytical results and numerically generated data has been represented graphically for frequencies, dissipation factor, displacements and temperature GRAPHICAL ABSTRACT

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Thermoelastic strain and stress fields due to a spherical inclusion in an elastic half-space

Cited by 3 publications

References 22 publications

Untitled

Untitled

On Graded S-Primary Submodules of Graded Modules Over Graded Commutative Rings

Analysis of Free Vibrations in Homogeneous Isotropic Rigidly Fixed Thermoelastic Circumferential Spherical Curved Plates

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