Study On Temperature Field Of Two-Dimensional Functionally Graded Cylinder By Finite Element Method

To research the two-dimensional steady and transient temperature field distributions of the two-dimensional FGM hollow cylinder under the first, third types of thermal boundary conditions, the physical parameters were assumed varying continuously and distributing arbitrarily along radial and axial direction. According to the three laws of thermodynamics and the material constitutive relation, starting from the equation of heat conduction and the corresponding functional, the finite element basic equation of the FGM hollow cylinder was established and the corresponding calculation program of FORTRAN was compiled.For one-dimensional axisymmetric heat conduction problem, the analytical solution using integral method and the numerical solution using finite element method was compared. and the results of two thermal conductivity models were compared. It is found that the results of two comparison methds are consistent. In addition, the finite element mesh was divided in the meridian plane of a cylinder, and the finite element mesh was encrypt from200to1600unit. The volume fraction of two-dimensional FGM cylinder is more accurate. Therefore, the correctness of the numerical solutions using finite element method was examined.Through the numerical results, the two-dimensional steady and transient temperature field distributions of two-dimensional FGM cylinder that consists of SiC, Al2O3, Al1100and Ti-6A1-4V under different boundary linear thermal loadings were obtained. The main research problems were as follows:(1) The influence of two dimensional FGM compositions on the two dimensional steady and transient temperature fields in the two dimensional FGM cylinder.(2) The influence of the form of the boundary thermal loading on the steady temperature fields in the one and two dimensional FGM cylinder.(3) The influence of the number of the material composition, boundary heat transfer coefficient and the thickness of the cylinder radial gradient on the two dimensional steady temperature fields in the two dimensional FGM cylinder.The main analysis results are as follows:(1) When nr is fixed and nz is changed, the maximum temperature difference value in low temperature area where metal is enriched increases by63.5%along the radial direction. The maximum temperature difference value in low temperature area where metal is enriched increases by70.9%compared with that in high temperature area where ceramic is enriched.(2) The temperature curve surface shapes have notable changes with the increase of the parameters nr and nz and especially when0.5≤z≤1.0. The maximum temperature difference value in high temperature area where ceramic is enriched reduces by37.5%along the radial direction, and the maximum temperature difference value in low temperature area where metal is enriched reduces by34.9%compared with that in high temperature area where ceramic is enriched along the radial direction.(3) With the increase of the thickness of the gradient layer along the radial direction of cylinder, the temperature value in high temperature area where ceramic is enriched decreases gradually and the temperature gradient increases gradually and the increase amplitude of the maximum temperature difference value reaches as high as24.7%.(4)The distribution of the temperature gradient in the temperature field consisting of four kinds of materials is more uniform than consisting of three kinds of materials.(5) With the increase of the convective heat transfer coefficient, the temperature values in the corresponding points increase gradually.(6) The two dimensional FGM cylinder is more suitable for bearing two dimensional boundary thermal loading.(7) The form of the boundary thermal loading has great effect on the two dimensional FGM steady temperature field.The above results may provide the foundations of the calculation for the heat-resistant protective material application of the aerospace engineering and further thermal stress analysis.