Plane Transient Cooling Thermal Stresses Of 2-FGM Plate Under Differentdisplacement Boundaries

In this paper, the research model is the two dimensional constant property functionally graded plates which are composed of Ti-6Al-4V, Al 1100 and ZrO2. Under the first kind of thermal boundary conditions, this paper has studied the influence of the displacement boundary on the transient cooling thermal stress of the plate.Based on the theory of continuum mechanics and the theory of thermal elasticity, and using the classical variational method, the finite element equations are derived and the program is written in FORTRAN language. In this program, the distribution law of the transient cooling thermal stress is obtained, and the influence of the displacement boundary on the transient cooling thermal stress of the 2D-FGM plate is also obtained.Analyzing the calculation results, the following conclusions can be obtained.(1) When the displacement boundary conditions are simply supported and cantilever, the absolute value of the stress lines in the plane will decrease gradually with the increase of cooling time. When the displacement boundary conditions are fixed at all ends and at the two sides, the absolute value of the stress lines in the plane will increase with the increase of the cooling time.(2) At the same cooling time, the average stress is the maximum when the displacement boundary condition is fixed at all ends; the average stress is the minimum when the displacement boundary condition is fixed at the two sides.(3) In the whole cooling process, the value of the stress lines is just positive when the displacement boundary conditions are fixed at all ends and at the two sides; the value of the stress lines have positive and negative values when the displacement boundary conditions are simply supported and cantilever. In addition, under different displacement boundary conditions, the change trend of stress lines is also close.By studying the influence of the displacement boundary conditions on the transient cooling thermal stress of the 2D-FGM plate, the displacement boundary conditions have a significant influence on the cooling thermal stress. Therefore, the results of this paper can provide reference for the application of functional gradient materials.