Analytical Solution Of Thermal Buckling Of Concrete Pavement

The thermal buckling of cement concrete pavement is one of the important problems that affect its performance.But at present,most of the existing research is the thin plate problem under the classical boundary condition,and the research on the complex elastic rotation constraint boundary condition is still less.Therefore,it is of great theoretical and engineering value to analyze the thermal buckling of elastic rectangular thin plates with complex boundary conditions.In this paper,the finite integral transformation method is used to study the analytical solution of thermal buckling of cement concrete pavement slab with complex boundary conditions.Firstly,the analytical solution of thermal buckling of elastic rectangular thin plates with four edges clamped is solved.On this basis,the cement concrete pavement slab constrained by the dowel bar is regarded as an elastic rectangular thin plate supported by spring on four sides.Then,the finite integral transformation method is used to solve the thermal buckling of the elastic rectangular plate with rotationally-restrained boundary condition.The example given in this paper illustrate that the method show satisfactory agreement with the finite element method,which verifies the accuracy and validity of the method.The convergence of the analytical solution is discussed and the result is good.The main research contents of this paper are as follows:1.This paper introduces how to use the finite integral transformation method to solve the thin plate problem and how to select the series kernel under different boundary conditions,summarizes the integral transformation kernel function under each boundary condition and explains the reasons.2.According to the classical Kirchhoff plate theory,the governing equation of thermal buckling of rectangular plate in constant temperature field is obtained.Aiming at the problem of plate with four sides fully-clamped boundary conditions,this paper selects the double sine series as the integral core.By finite integral transformation of the governing equation,the problem can be transformed into solving simple linear algebraic equations.Finally,the solution of the related problem is obtained by using the corresponding inverse transformation expression.This method reduces the difficulty of solving the temperature buckling problem.3.By introducing the coefficient of spring rotation,this paper studies the thermal buckling of thin plates under the condition of homogeneous elastic rotation boundary.The analytical solution of this kind of complex boundary condition can be obtained by the similar solution process with four sides fully-clamped.In addition,by adjusting the spring coefficient,the solution of the problem under various classical boundary conditions can be obtained.The results obtained in this paper are in good agreement with the numerical results of the existing finite element simulation,and the validity of the solution is verified.