This paper is concerned with the determination of thermoelastic displacement, stress and temperature in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity, in the context of ...This paper is concerned with the determination of thermoelastic displacement, stress and temperature in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters （Green and Lindsay theory）. The surface of cavity is stress-free and is subjected to a time-dependent thermal shock. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. Numerical inversion of the transforms is carried out using the Bellman method. Displacement, stress and temperature are computed and presented graphically. It is found that variation in the thermo-physical properties of a material strongly influences the response to loading. A comparative study with a corresponding homogeneous material is also made.展开更多
The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate a...The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically.展开更多
文摘This paper is concerned with the determination of thermoelastic displacement, stress and temperature in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters （Green and Lindsay theory）. The surface of cavity is stress-free and is subjected to a time-dependent thermal shock. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. Numerical inversion of the transforms is carried out using the Bellman method. Displacement, stress and temperature are computed and presented graphically. It is found that variation in the thermo-physical properties of a material strongly influences the response to loading. A comparative study with a corresponding homogeneous material is also made.
文摘The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically.
