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
基金Supported by the National Nature Science Foundation of China(61074091)the Project of Outstanding Young and Middle-aged Scientific and Technological Innovation Team of Colleges and Universities in Hubei Province(T201103)
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.
