Study On Steady Temperature Field Of 2D-FGM Plate Under Complex Thermal Boundary

Functionally graded material(FGM)is a new type of heterogeneous composite material,which adopts advanced material composite technology to make its components,structure and physical parameters change continuously in the structure.It can effectively eliminate the interface effect of composite materials,avoid the stress mutation and jump between different material combinations,and fundamentally solve the interface problem of material composite to adapt to different environments.Because of its excellent structure and properties,it has been widely applied in the field of aerospace,nuclear power,mechanical design,biological science and other ultra high temperature,large temperature difference and corrosive environment.Based on heat transfer,thermoelasticity and finite element method,the steady-state temperature field of 2D-FGM plate under the left and right side are the first kind of boundary condition,the lower side is the second kind of boundary condition,the upper side is the third kind of boundary condition is studied.First,starting from the law of thermodynamics and Fourier law,the steady state heat conduction differential equation of 2D-FGM plate is obtained.Then the analytical solution of steady state temperature field of 2D-FGM plate under three kinds of boundary conditions is derived by using the method of separation of variables.Secondly,using the weighted residual method,the heat conduction differential equation of the finite element form is derived,and the steady heat transfer value solution of the 2D-FGM plate is obtained.The results of the two methods are compared,the error is less than 1%,which can verify the correctness of the derivation process.Finally,the influence of the gradient parameters of the thermal conductivity of the material,the temperature of the upper boundary medium and the heat flux of the lower boundary on the steady temperature field of the 2D-FGM plate is analyzed.The following conclusions are drawn: The steady-state temperature distribution of 2D-FGM plate is approximately four angular stellate,which is not symmetrical;The heat is inflow into the plate from the upper and lower sides of the plate,and then from the left and right sides of the plate to the outside of the plate;With the increase of the gradient parameters c and d,the maximum temperature on the upper and lower edges of the plate decreases;The increase of the temperature of the upper boundary medium has a great influence on the maximum temperature on the upper and lower edges of the plate.The increase of the heat flux at the lower boundary has a great effect on the maximum temperature of the lower edge of the plate,but has little effect on the upper edge.The results provide a practical and accurate theoretical basis for future development,optimization design and engineering application,and provide an important reference for further research and development of FGM.