According to the two-dimensional(2-D) thermo-elasticity theory, the exact elasticity solution of the simply supported laminated beams subjected to thermo-loads was studied. An analytical method was presented to obtain...According to the two-dimensional(2-D) thermo-elasticity theory, the exact elasticity solution of the simply supported laminated beams subjected to thermo-loads was studied. An analytical method was presented to obtain the temperature, displacement and stress fields in the beam. Firstly, the general solutions of temperature, displacements and stresses for a single-layered simply supported beam were obtained by solving the 2-D heat conduction equation and the 2-D elasticity equations, respectively. Then, based on the continuity of temperature, heat flux, displacements and stresses on the interface of two adjacent layers, the formulae of temperature, displacements and stresses between the lowest layer and the top layer of the beam were derived out in a recurrent manner. Finally, the unknown coefficients in the solutions were determined by the use of the upper surface and lower surface conditions of the beam. The distributions of temperature, displacement and stress in the beam were obtained by substituting these coefficients back to the recurrence formulae and the solutions. The excellent convergence of the present method has been demonstrated and the results obtained by the present method agree well with those from the finite element method. The effects of surface temperatures, thickness, layer number and material properties of the plate on the temperature distribution were discussed in detail. Numerical results reveal that the displacements and stresses monotonically increase with the increase of surface temperatures. In particular, the horizontal stresses are discontinuous at the interface.展开更多
We study a new model named the Green-Lindsay type therm-elastic model for nonhomogeneous media that consists of a system of dynamic thermoelasticity equations of displacement and dynamic heat conduction equation. We c...We study a new model named the Green-Lindsay type therm-elastic model for nonhomogeneous media that consists of a system of dynamic thermoelasticity equations of displacement and dynamic heat conduction equation. We construct the model based on the classical GL-model for homogeneous material. This system is coupled dynamic problem and the displacement field and heat field must be solved at the same time. By using Fadeo- Galerkin method, we proved that the problem we proposed exist unique weak solution under some regular assumption.展开更多
This paper demonstrates the plane stress state and the stress free thermo-elastic deformation of FGM thick plate under thermal loading.First,the Sneddon-Lockett theorem on the plane stress state in an isotropic infini...This paper demonstrates the plane stress state and the stress free thermo-elastic deformation of FGM thick plate under thermal loading.First,the Sneddon-Lockett theorem on the plane stress state in an isotropic infinite thick plate is generalized for a case of FGM problem in which all thermo-mechanical properties are optional functions of depth co-ordinate.The proof is based on application of the Iljushin thermo-elastic potential to displacement type system of equations that reduces it to the plane stress state problem.Then an existence of the purely thermal deformation is proved in two ways:first,it is shown that the unique solution fulfils conditions of simultaneous constant temperature and linear gradation of thermal expansion coefficient,second,proof is based directly on stress type system of equations which straightforwardly reduces to compatibility equations for purely thermal deformation if only stress field is homogeneous in domain and at boundary.Finally,couple examples of application to an engineering problem are presented.展开更多
基金Project(2012CB026205)supported by the National Basic Research Program of ChinaProject(51238003)supported by the National Natural Science Foundation of ChinaProject(2014Y01)supported by the Transportation Department of Jiangsu Province,China
文摘According to the two-dimensional(2-D) thermo-elasticity theory, the exact elasticity solution of the simply supported laminated beams subjected to thermo-loads was studied. An analytical method was presented to obtain the temperature, displacement and stress fields in the beam. Firstly, the general solutions of temperature, displacements and stresses for a single-layered simply supported beam were obtained by solving the 2-D heat conduction equation and the 2-D elasticity equations, respectively. Then, based on the continuity of temperature, heat flux, displacements and stresses on the interface of two adjacent layers, the formulae of temperature, displacements and stresses between the lowest layer and the top layer of the beam were derived out in a recurrent manner. Finally, the unknown coefficients in the solutions were determined by the use of the upper surface and lower surface conditions of the beam. The distributions of temperature, displacement and stress in the beam were obtained by substituting these coefficients back to the recurrence formulae and the solutions. The excellent convergence of the present method has been demonstrated and the results obtained by the present method agree well with those from the finite element method. The effects of surface temperatures, thickness, layer number and material properties of the plate on the temperature distribution were discussed in detail. Numerical results reveal that the displacements and stresses monotonically increase with the increase of surface temperatures. In particular, the horizontal stresses are discontinuous at the interface.
基金Foundation item： Supported by the National Natural Science Foundation of China（10771198）
文摘We study a new model named the Green-Lindsay type therm-elastic model for nonhomogeneous media that consists of a system of dynamic thermoelasticity equations of displacement and dynamic heat conduction equation. We construct the model based on the classical GL-model for homogeneous material. This system is coupled dynamic problem and the displacement field and heat field must be solved at the same time. By using Fadeo- Galerkin method, we proved that the problem we proposed exist unique weak solution under some regular assumption.
文摘This paper demonstrates the plane stress state and the stress free thermo-elastic deformation of FGM thick plate under thermal loading.First,the Sneddon-Lockett theorem on the plane stress state in an isotropic infinite thick plate is generalized for a case of FGM problem in which all thermo-mechanical properties are optional functions of depth co-ordinate.The proof is based on application of the Iljushin thermo-elastic potential to displacement type system of equations that reduces it to the plane stress state problem.Then an existence of the purely thermal deformation is proved in two ways:first,it is shown that the unique solution fulfils conditions of simultaneous constant temperature and linear gradation of thermal expansion coefficient,second,proof is based directly on stress type system of equations which straightforwardly reduces to compatibility equations for purely thermal deformation if only stress field is homogeneous in domain and at boundary.Finally,couple examples of application to an engineering problem are presented.
