Analytical Solution To The Multilayered Elastic System With Functionally Graded Materials

Since the reform and opening up in the last century,China's road construction has been booming and achieved remarkable achievements.The total mileage of highways ranks first in the world.However,the highways at all levels not only undergo the driving load,but also are affected by the environment,especially the climatic temperature cycle and the oxidative aging effect,which causes the gradient of the modulus of elasticity of the asphalt.The current solution to the mechanical response of the functional gradient of asphalt pavement materials is mainly solved by finite element method and other numerical methods.In order to solve the analytic solution of functionally graded pavement,the paper derives the ordinary differential equations of the functionally gradient multilayered elastic system from the vector function system,and uses the transfer matrix method and the stiffness matrix method to find out the analytical solution.On this basis,a new solution method for the dual boundary of the dual vector is proposed.The main contents are as follows:(1)For the functionally gradient multi-layer pavement structure system with circular uniformly distributed surface loading,the expressions of the ordinary differential equations of the mechanical control equations of functionally graded pavement structures are deduced using the vector function system in the cylindrical coordinate system.The propagation matrix and stiffness matrix are used to solve the above ordinary differential equations.(2)On the basis of the above,combined with the advantages of the stiffness matrix method and the fact that the upper and lower boundaries are dually presented,an analytical solution of the mechanical response of the functionally graded pavement structure with the dual vector dual boundary is proposed.(3)Using numerical examples,the correctness of the three methods was compared and analyzed.At the same time,the advanced results of mechanical response analysis of pavement structures with functionally graded material was further confirmed.The results show that the response of the functionally graded materials are more consistent with the actual road conditions.The solution to the response of multi-layer elastic system with functionally graded materials can urge and consummate the existing theory for road structure design,and it is of great significance to analyze the practical engineering road structure performance.