Analytical Solution To The Multilayered Elastic System With Consideration Of Temperature

Road transportation is one of the main modes of land transportation,which is closely related to people's life.Among them,asphalt pavement is widely used in road structure because of its many advantages.However,it should be noted that asphalt pavement is exposed to the natural environment after service,it will not only be affected by the driving load,but also influenced by continuously changing external environmental factors,such as solar radiation,ground reflection,atmospheric temperature,precipitation and so on.The heat generated by these environmental factors on the road surface is transmitted downward along the depth direction of the road through the heat conduction,which results in the temperature changes at different depths of the road structure,and further causes the temperature stress to have a negative impact on the service performance and durability of the road surface.Therefore,in order to fully understand the mechanical characteristics of the road structure,it is necessary to study the response of the road structure under the action of temperature and the change of the material properties,so as to provide technical reference for the rational selection of the asphalt pavement structure and materials,which is of great significance for improving the service performance and durability of the road.In this paper,the multilayered elastic system with cylindrical coordinates is taken as the calculation model,and the basic equation for solving the problem is established by using the theory of thermoelastic mechanics.In order to simplify the partial differential equation in the basic equation,the integral transformation of Laplace is firstly applied to the governing equation to eliminate the time variable t.Then the vector function system is introduced to derive the ordinary differential equation.On this basis,according to the characteristics of dual boundary,the propagation matrix method,stiffness matrix method and dual vector method are used to solve the problem.Finally,the final solution is obtained by the inversion of Laplace transformation.The paper also considers and proves the rationality of Laplace inverse transform technology,such as Durbin,Talbot,Zakian,etc.,and uses FORTRAN language for programming and numerical cases analysis.The example shows that the dual vector dual boundary method based on Talbot has better applicability and higher accuracy to solve the problem of temperature field and temperature stress in layered system.Thetransfer of temperature in the pavement structure is a process of attenuation,with a certain depth of influence.The temperature stress on the pavement surface is the largest,with the increase of depth,the temperature stress gradually decreases.Compared with the pavement surface,the temperature peak of each layer has a certain lag with the increase of depth,and the greater the depth is,the longer the lag time is.The temperature stress also has the same change rule with the temperature.