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Two-Temperature Generalized Thermopiezoelasticity for One Dimensional Problems – State Space Approach

Youssef H. M., Bassiouny E.

Computational Methods in Science and Technology

2008

Vol. 14, nr 1

55-64

The theory of two-temperature generalized thermoelasticity, based on the theory of Youssef is used to solve boundary value problems of one dimensional piezoelectric half-space with heating its boundary with different types of heating. The governing equations are solved in the Laplace transform domain by using state-space approach of the modern control theory. The general solution obtained is applied to a specific problems of a half-space subjected to three types of heating; the thermal shock type, the ramp type and the harmonic type. The inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. The conductive temperature, the dynamical temperature, the stress and the strain distributions are shown graphically with some comparisons.

Thermal Shock Problem of Generalized Thermoelasticity for an Infinitely Long Annular Cylinder with Variable Thermal Conductivity

Youssef H. M., Abbas I. A.

Computational Methods in Science and Technology

2007

Vol. 13, nr 2

95-100

In this paper, a general finite element model is proposed to analyze transient phenomena in thermoelastic model in the context of the theory of generalized thermoelasticity with one relaxation time with variable thermal conductivity. An application of an infinitely long annular cylinder was studied, where the inner surface is traction free and subjected to thermal shock, while the outer surface is traction free and thermally isolated. The results for the temperature increment, the stress components and the displacement component are illustrated graphically.