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Nonlinear coupled thermoelastic analysis of thermal wave propagation in a functionally graded finite solid undergoing finite strain

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Abstract

In this research, a study of nonlinear thermoelastic, transient responses and thermal wave propagation of functionally graded (FG) finite length solid under a thermal shock and surface stress loading is carried out. The coupled equations are derived from the concept of large displacement as well as finite strains. Therefore, the nonlinear Lagrangian strain–displacement expression and second Piola–Kirchhoff stress are employed in that the components of displacement and stresses are obtained in the original coordinate. Besides, the assumption of very small temperature changes compared to the reference temperature is released in the present research. The thermal wave propagation is discussed for surface stress traction and thermal shock. The thermal stress, displacement and temperature distributions are illustrated graphically for some grading patterns of FG solid, and the effects of grading patterns of the material properties on wave propagation are investigated. The obtained results indicate significant effects of volume fraction on stress and thermal wave propagation of a medium under mechanical and thermal loading. Moreover, the results show that the increase in volume fraction leads to increase in the wave speed in both different conditions.

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Abbreviations

b :

Body force, intrinsic energy

\(c_{\upvarepsilon}\) :

Specific heat capacity

E :

Green’s strain tensor

F :

Deformation gradient

h :

Heat transfer coefficient

K :

Thermal conductivity

\(l_{\text{e}}\) :

Element length

L :

Medium length

\(p_{\text{m}}\) :

Metal properties

\(p_{\text{c}}\) :

Ceramic properties

q :

Heat flux

r :

Heat generation per unit mass

T :

Temperature

\(T_{0}\) :

Reference temperature

t :

Time

U(X,t):

Displacement vector

\(v\) :

Wave velocity

X :

Reference coordinate

\(\alpha_{\text{T}}\) :

Thermal expansion coefficient

δ :

Delta function

σ :

Traction

\(\Delta t\) :

Time increment

ρ 0 :

Density

μ :

Shear modulus

λ :

Lame constants

\( \psi_{\text{j}}^{{\text{e}}} (x) \) :

Shape functions

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Authors and Affiliations

  1. Department of Mechanical Engineering, Yazd University, Yazd, Iran

    M. Mirparizi & A. R. Fotuhi

  2. Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran

    M. Shariyat

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  1. M. Mirparizi
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  3. M. Shariyat
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Correspondence to A. R. Fotuhi.

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Mirparizi, M., Fotuhi, A.R. & Shariyat, M. Nonlinear coupled thermoelastic analysis of thermal wave propagation in a functionally graded finite solid undergoing finite strain. J Therm Anal Calorim 139, 2309–2320 (2020). https://doi.org/10.1007/s10973-019-08652-4

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