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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

Citations:

Zbl 0147.14003

Software:

MatWeb
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Full Text: DOI

References:

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