scholarly journals FRACTIONAL ORDER THEORY OF THERMAL STRESSES IN A TWO DIMENSIONAL TRANSVERSELY ISOTROPIC MAGNETO THERMOELASTIC MATERIAL

2020 ◽  
Vol 50 (3) ◽  
Author(s):  
PARVEEN LATA ◽  
IQBAL KAUR
Keyword(s):  
Fractional Order ◽  
Thermal Stresses ◽  
Transversely Isotropic ◽  
Order Theory ◽  
Two Dimensional ◽  
Thermoelastic Material

Fundamental solution for a two-dimensional problem in transversely isotropic micropolar thermoelastic media

2017 ◽  
Vol 13 (3) ◽  
pp. 409-423 ◽  
Author(s):  
Vijay Chawla ◽  
Sanjeev Ahuja ◽  
Varsha Rani
Keyword(s):  
General Solution ◽  
Fundamental Solution ◽  
Heat Source ◽  
Harmonic Functions ◽  
Transversely Isotropic ◽  
Fundamental Solutions ◽  
Two Dimensional ◽  
Point Heat Source ◽  
Content Type ◽  
Thermoelastic Material

Purpose The purpose of this paper is to study the fundamental solution in transversely isotropic micropolar thermoelastic media. With this objective, the two-dimensional general solution in transversely isotropic thermoelastic media is derived. Design/methodology/approach On the basis of the general solution, the fundamental solution for a steady point heat source on the surface of a semi-infinite transversely isotropic micropolar thermoelastic material is constructed by six newly introduced harmonic functions. Findings The components of displacement, stress, temperature distribution and couple stress are expressed in terms of elementary functions. From the present investigation, a special case of interest is also deduced and compared with the previous results obtained. Practical implications Fundamental solutions can be used to construct many analytical solutions of practical problems when boundary conditions are imposed. They are essential in the boundary element method as well as the study of cracks, defects and inclusions. Originality/value Fundamental solutions for a steady point heat source acting on the surface of a micropolar thermoelastic material is obtained by seven newly introduced harmonic functions. From the present investigation, some special cases of interest are also deduced.

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

2020 ◽  
Vol 25 (3) ◽  
pp. 169-180
Author(s):  
S. Thakare ◽  
Y. Panke ◽  
K. Hadke
Keyword(s):  
Temperature Distribution ◽  
Fractional Order ◽  
Heat Supply ◽  
Numerical Evaluation ◽  
Thermal Stresses ◽  
Order Theory ◽  
Curved Surface ◽  
Mathieu Function ◽  
Zero Temperature ◽  
Thermal Deflection

AbstractIn 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.

Two-Dimensional Poroelastic Problem for Saturated Soil Under Fractional Order Theory of Thermoelasticity

2022 ◽  
Author(s):  
Ying Guo ◽  
Chunbao Xiong ◽  
Jianjun Ma ◽  
Da Li ◽  
Chaosheng Wang
Keyword(s):  
Fractional Order ◽  
Order Theory ◽  
Saturated Soil ◽  
Two Dimensional

scholarly journals Fractional order elliptic problems with inhomogeneous Dirichlet boundary conditions

2020 ◽  
Vol 23 (2) ◽  
pp. 378-389
Author(s):  
Ferenc Izsák ◽  
Gábor Maros
Keyword(s):  
Fractional Order ◽  
Boundary Data ◽  
Dirichlet Boundary ◽  
Elliptic Problems ◽  
Integral Form ◽  
Uniqueness Result ◽  
Boundary Integral ◽  
Dirichlet Boundary Conditions ◽  
Two Dimensional ◽  
Potential Operators

AbstractFractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping properties of the corresponding potential operators. The existence-uniqueness result is stated also for two-dimensional domains. Finally, a mild condition is provided to ensure the existence of the classical solution of the boundary integral equation.

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