Heat Conduction Investigation Of The Functionally Graded Structure Based On Hybrid Numerical Method

Functionally graded materials(FGM)is a newly development material in recent years.Its distinguishing feature is that the composition of the material presents a continuous gradient change in the thickness direction.The feature and function of the material also appear a gradient change.Therefor,the thermal stress and residual stress of material can be relieved.Due to its superior physical properties,it is widely used in the high temperature environment.Thus,it is especially important for analyzing the distribution characteristics of the temperature and the characteristics of heat conduction.Since the variable physical parameters in the functionally graded structure,the analytical solutions are too difficult to get for the complex heat conduction problems.The precision of the research will be declined,and the computational memory is limited while using numerical method.The hybrid numerical method combines the advantages of analytical method and numerical method,which is widely used in the dynamics analysis for composition materials.In this paper,the infinite functionally gradient structure plate is considered,and the hybrid numerical method is used to study the heat conduction problem of functionally graded structure with variable gradient parameters under exponential heat source load.The functionally graded material model is discretized into layers along the thickness direction by interpolation in a coordinate direction using the numerical method.The other coordinate direction is solved theoretically according to the Fourier transform method,and then the solution in the whole domain of the model is obtained,which combined the accuracy of the analytical method with the efficiency of the numerical method.The main work of this paper is as follows:In this paper,the two-dimensional differential equation of heat conduction withfunctionally gradient structure was constructed by Fourier law,which based on the differential equation of micro-body heat balance.And then shape function was constructed.The hybrid numerical method theory was established through the method of weighted residual,which considering the convective heat transfer boundary condition.Then we derived the temperature function of the linear functionally gradient structure plate under exponential heat source load.Meanwhile,we used the finite element method to solve the heat conduction problem of pure metal material and verified the results of the hybrid numerical method.The results show that the hybrid numerical method is consistent with the finite element method in solving the heat conduction problem of functionally gradient structures.Furthermore,the temperature distribution of the functionally gradient structure was obtained by solving the temperature function,and studied the variation of temperature in the time domain and position domain at different position under the exponential heat source loaded.Furtherly,the hybrid numerical method was extended to solve the heat conduction problem of functionally graded structures with variable gradient parameters.The parameterized model of functional gradient structure with variable gradient parameters was established.And achieved the material components are changed by controlling the different gradient parameters in the model.Then adopted the hybrid numerical method to research the heat conduction of functionally graded structures plates with variable gradient parameters under the exponential heat source load,and obtained the temperature distribution of the FGM plates with variable gradient parameters.Furthermore,we studied The relationship between gradient parameters and temperature distribution in model.The results show that influence of the heat source in model is only partial,the distribution of the temperature is gradually reducing with the distance away from the heat source,and it tends to zero in infinite distance position.The change of the gradient parameter in a certain range has a great influence on the heat conduction,when the gradient parameters are maximization and minimization,the heat conduction becomes the heat conduction process of pure materials.In this paper,the heat conduction of the functional gradient plate with different gradient parameters is numerically simulated,and obtained the temperature distribution at different positions in the model.All the results are consistent and in line with the actual situation,and the results are consistent with the finite element results.It shows that the hybrid numerical method is reasonable and provides a new way for solving the heat conduction of FGM plats with variable gradient parameters.