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.


74D05 Linear constitutive equations for materials with memory
74F05 Thermal effects in solid mechanics


Zbl 0147.14003


Full Text: DOI


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