The thermoelastic interaction for the three-phase-lag （TPL） heat equation in an isotropic infinite elastic body with a spherical cavity is studied by two-temperature generalized thermoelasticity theory （2TT）. The ...The thermoelastic interaction for the three-phase-lag （TPL） heat equation in an isotropic infinite elastic body with a spherical cavity is studied by two-temperature generalized thermoelasticity theory （2TT）. The heat conduction equation in the theory of TPL is a hyperbolic partial differential equation with a fourth-order derivative with respect to time. The medium is assumed to be initially quiescent. By the Laplace trans- formation, the fundamental equations are expressed in the form of a vector-matrix differ- ential equation, which is solved by a state-space approach. The general solution obtained is applied to a specific problem, when the boundary of the cavity is subjected to the ther- mal loading （the thermal shock and the ramp-type heating） and the mechanical loading. The inversion of the Laplace transform is carried out by the Fourier series expansion tech- niques. The numerical values of the physical quantity are computed for the copper like ma- terial. Significant dissimilarities between two models （the two-temperature Green-Naghdi theory with energy dissipation （2TGN-III） and two-temperature TPL model （2T3phase）） are shown graphically. The effects of two-temperature and ramping parameters are also studied.展开更多
This paper deals with the determination of the thermo-elastic displacements and stresses in a multi-layered body set up in different layers of different thickness having different elastic properties due to the applica...This paper deals with the determination of the thermo-elastic displacements and stresses in a multi-layered body set up in different layers of different thickness having different elastic properties due to the application of heat and a concentrated load in the uppermost surface of the medium. Each layer is assumed to be made of homogeneous and isotropic elastic material. The relevant displacement components for each layer are taken to be axisymmetric about a line, which is perpendicular to the plane surfaces of all layers. The stress function for each layer, therefore, satisfies a single equation in absence of any body forces. The equation is then solved by integral transform technique. Analytical expressions for thermo-elastic displacements and stresses in the underlying mass and the corresponding numerical codes are constructed for any number of layers. However, the numerical comparison is made for three and four layers.展开更多
文摘The thermoelastic interaction for the three-phase-lag （TPL） heat equation in an isotropic infinite elastic body with a spherical cavity is studied by two-temperature generalized thermoelasticity theory （2TT）. The heat conduction equation in the theory of TPL is a hyperbolic partial differential equation with a fourth-order derivative with respect to time. The medium is assumed to be initially quiescent. By the Laplace trans- formation, the fundamental equations are expressed in the form of a vector-matrix differ- ential equation, which is solved by a state-space approach. The general solution obtained is applied to a specific problem, when the boundary of the cavity is subjected to the ther- mal loading （the thermal shock and the ramp-type heating） and the mechanical loading. The inversion of the Laplace transform is carried out by the Fourier series expansion tech- niques. The numerical values of the physical quantity are computed for the copper like ma- terial. Significant dissimilarities between two models （the two-temperature Green-Naghdi theory with energy dissipation （2TGN-III） and two-temperature TPL model （2T3phase）） are shown graphically. The effects of two-temperature and ramping parameters are also studied.
文摘This paper deals with the determination of the thermo-elastic displacements and stresses in a multi-layered body set up in different layers of different thickness having different elastic properties due to the application of heat and a concentrated load in the uppermost surface of the medium. Each layer is assumed to be made of homogeneous and isotropic elastic material. The relevant displacement components for each layer are taken to be axisymmetric about a line, which is perpendicular to the plane surfaces of all layers. The stress function for each layer, therefore, satisfies a single equation in absence of any body forces. The equation is then solved by integral transform technique. Analytical expressions for thermo-elastic displacements and stresses in the underlying mass and the corresponding numerical codes are constructed for any number of layers. However, the numerical comparison is made for three and four layers.
