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**Generalized thermo-visco-elastic problem of a spherical shell with three-phase-lag effect.**
*(English)*
Zbl 1205.74021

Summary: This problem deals with the thermo-visco-elastic interaction due to step input of temperature on the stress free boundaries of a homogeneous visco-elastic isotropic spherical shell in the context of generalized theories of thermo-elasticity. Using the Laplace transformation the fundamental equations have been expressed in the form of vector-matrix differential equation which is then solved by eigen value approach. The inverse of the transformed solution is carried out by applying a method of R. Bellmen, R.E. Kolaba and J.A. Lockette [Numerical inversion of the Laplace transform: Applications to biology, economics, engineering, and physics. Modern Analytic and Computational Methods in Science and Mathematics. 4. American Elsevier Publishing Company (1966; Zbl 0147.14003)]. The stresses are computed numerically and presented graphically in a number of figures for copper material. A comparison of the results for different theories (TEWED (GN-III), three-phase-lag method) is presented. When the body is elastic and the outer radius of the shell tends to infinity, the corresponding results agree with the result of existing literature.

### MSC:

74D05 | Linear constitutive equations for materials with memory |

74F05 | Thermal effects in solid mechanics |

### Keywords:

generalized thermo-visco-elasticity; energy dissipation; Laplace transform; step input temperature; vector-matrix differential equation; three-phase-lag model### Citations:

Zbl 0147.14003### Software:

MatWeb
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\textit{A. Kar} and \textit{M. Kanoria}, Appl. Math. Modelling 33, No. 8, 3287--3298 (2009; Zbl 1205.74021)

Full Text:
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### References:

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