Heat source problem of thermoelasticity in an elliptic plate with thermal bending moments

Bhad, Pravin; Varghese, Vinod; Khalsa, Lalsingh

doi:10.1080/01495739.2016.1211496

Cited by 8 publications

(7 citation statements)

References 4 publications

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“…where E denotes the Young modulus and  is the coefficient of linear thermal expansion of the material of the disk, respectively. The governing differential equation for the disk in terms of normal deflection ( , , ) [23] as…”

Section: Thermal Deflection and Thermal Stressesmentioning

confidence: 99%

“…Gupta [22] determined the boundary value problem for elliptic cylinders by introducing a finite transform involving Mathieu functions. Bhad [23] investigated the thermoelastic problems on an elliptical plate in which interior heat sources are generated within the solid. Dhakate [24] used Berger's approximate methods to determine the large deflection of a heated thin annular sector plate with clamped edges under transient temperature distribution.…”

Section: Introductionmentioning

confidence: 99%

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Application of Fractional Order Theory of Thermoelasticity in an Elliptical Disk and Associated Thermal Stresses

Thakare¹,

Panke²,

Hadke³

2020

International Journal of Applied Mechanics and Engineering

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In this article, a time fractional-order theory of thermoelasticity is applied to an isotropic homogeneous elliptical disk. The lower and upper surfaces of the disk are maintained at zero temperature, whereas the sectional heat supply is applied on the outer curved surface. Thermal deflection and associated thermal stresses are obtained in terms of Mathieu function of the first kind of order 2n. Numerical evaluation is carried out for the temperature distribution, Thermal deflection and thermal stresses and results of the resulting quantities are depicted graphically.

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Section: Thermal Deflection and Thermal Stressesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Application of Fractional Order Theory of Thermoelasticity in an Elliptical Disk and Associated Thermal Stresses

Thakare¹,

Panke²,

Hadke³

2020

International Journal of Applied Mechanics and Engineering

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“…Roy Choudhary [3], Khobragade and Deshmukh [4], Varghese and Khalsa [5] and many others. Similarly, the present author [6][7][8][9][10][11][12][13] have investigated various thermoelastic problems in elliptical objects of simple materials due to interior heat generation or sectional heat supply with different solid objects. Even one-dimensional thermoelastic problems made up of non-simple elastic material due to heat sources has been studied by various authors, viz.…”

Section: Introductionmentioning

confidence: 99%

Temperature and stress distribution in a non-simple elastic elliptical plate due to point impulsive heat sources

Varghese¹,

Bhad²,

Mahakalkar³

2019

International Journal of Thermodynamics

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The paper attempts to determine the thermoelastic stresses in a thin elliptical plate made up of non-simple elastic material subjected to point impulsive time-dependent source of heat moving with constant velocity over the specified finite portion. The temperature field in the plate has been considered when the sectional heat supply is continuously distributed along the circumference of an ellipse over the upper face with zero temperature on the lower face, and thermally insulated curved edge. The solution is formulated involving the Mathieu and modified functions by employing the Laplace transform technique. The analytical solution for the thermal stress components is obtained using Airy's stress function with mechanical boundary conditions as stress-free. Numerical results are also obtained.

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“…moreover,  M is bending of the plate due to change in the temperature and expressed as Furthermore, the thermal stress components in terms of resultant forces and resultant moments are given [11,12] as…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Most of the studies considered by authors above have examined the bending of an elliptical structural element subjected to the combined action of uniform lateral load and in-plane force treated in terms of the exact analytical method in case of simply supported so as to rotate freely. Bhad et al [11] investigated the thermoelastic problems on an elliptical plate in which internal heat sources are generated within the solid, with compounded effect due to sectional heating and boundary conditions of the Dirichlet type based on the theory of integral transformations. However, till date, nobody has studied any thermoelastic problem for elliptical plates with boundary conditions as mixed type, in which plates are considered to be fixed and clamped.…”

Section: Introductionmentioning

confidence: 99%

Transient thermal stresses of annulus elliptical plate with mixed-type boundary conditions.

Bhad¹

2017

International Journal of Thermodynamics

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In this paper, we consider a transient thermal stress investigation into an annulus thin elliptical plate in which edges are fixed and clamped. The realistic problem of the plate is supposed with mixed-type boundary conditions subjected to arbitrary initial temperature on the upper face, and the lower face is kept at zero temperature. Things get further complicated when internal heat generation persists in the object and further becomes unpredictable when sectional heat supply is impacted on the body. The solution to conductivity equation and the corresponding initial and boundary conditions is solved by employing a new integral transform technique. The governing equation for small deflection is found and utilized to preserve the intensities of thermal bending moments and twisting moments, involving the Mathieu and modified functions and their derivatives. It was found that the deflection result nearly agrees with the previously given result. Thus, the numerical results obtained are accurate enough for practical purposes. Conclusions emphasize the importance of better understanding the underlying elliptic structure, improved understanding of its relationship to circular object profile, and better estimates of the thermal effect of the thermoelastic problem.

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Heat source problem of thermoelasticity in an elliptic plate with thermal bending moments

Cited by 8 publications

References 4 publications

Application of Fractional Order Theory of Thermoelasticity in an Elliptical Disk and Associated Thermal Stresses

Application of Fractional Order Theory of Thermoelasticity in an Elliptical Disk and Associated Thermal Stresses

Temperature and stress distribution in a non-simple elastic elliptical plate due to point impulsive heat sources

Transient thermal stresses of annulus elliptical plate with mixed-type boundary conditions.

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