Effect Of Boundary Temperature On Transient Cooling Thermal Stress Field Of Two Dimensional Functionally Graded Plate

Based on the research of current situation about functionally graded materials, a finite element analysis of 2D-FGM plane transient thermal stress field under the influence of the boundary temperature during cooling process is proposed in this paper.Combined with Fourier’s law and the first law of thermodynamics, two-dimensional heat conduction equations are derived. According to the general procedure for solving finite element method, the two-dimensional finite element equations of heat conduction can be solved with the structure meshing, and combined conditions of two-dimensional heat transfer boundary, the corresponding temperature fields are obtained. In order to ensure the convergence of finite element solution, the displacement interpolation function is introduced. When analysising an unit, the relationship between nodal forces and nodal displacements of corresponding unit is obtained, and summing strain potential caused by the nodal displacements, plane thermal stress finite element basic equations can be obtained combined with total potential energy of expression. Model of this paper is FGM plate structures which is not considered temperature-dependent material properties and constituted of Al 1100/Ti-6Al-4V/Zr O2, under the conditions of constant porosity, components and displacement boundary, FGM physical parameters which are based on Kerner mesomechanics model are provided, the cooling transient thermal stress finite element program are obtained with FORTRAN, and the validity of finite element procedure is testified by contrasting analytic and numerical results. Finally, the regularities of cooling transient thermal stress are analyzed according to the results of the program solving.The temperature field calculation results of the 2D-FGM plate with the different heating boundary conditions on the upper boundary show that positive stress is generated in the cooling process, and stress of the plate is concentrated to the area where the temperature is high, the influence of constant temperature function in the plate is more obvious than others. With the increase of boundary temperature, the maximum aggrandizing rate of the stress attained to 150%, and the minimum attained to 76.89%.The results which different heating boundary conditions on the upper boundary with fixed temperature value on the lower boundary, and different heating boundary conditions on the upper boundary with fixed temperature value on the other three sides boundary are similar to the above. However, the internal stress concentration positions is different.In practice, therefore, this paper has important reference significance to the design of 2D-FGM plate with the different temperature boundary conditions.