Generalized Finite Integral Transform Method For Analytical Calculation Of Concrete Pavement Plates

In this paper,cement concrete pavement is considered as elastic rectangular thin plate.With generalized finite integral transform method,the analytic solution of critical load in concrete pavement with four clamped supported edges under the condition of buckling and vibration is derived.Integral transformation is one of the effective means to solve partial differential equations,but the traditional finite integral transform method is only applicable to simple boundary condition with four simply supported edges.In order to solve the problem of elastic plate with complex boundary condition by finite integral transform method,the generalized finite integral transform method is established in this paper.By using this method,the integral kernel is directly selected to satisfy different boundary conditions,and the high order partial differential equation describing the elastic plate buckling is transformed into the ordinary differential equation,which is finally transformed into the linear algebraic equation,and the analytic solution to the elastic plate buckling and vibration problem is derived.The main research content of this paper are as follows:(1)Firstly,the generalized finite integral transformation method is established.Based on the natural vibrational solution of beam,the shape function is satisfied under different boundary conditions,and take it as the integral kernel of the generalized finite integral transform method.We calculate the natural vibrational solution of simply supported beam,clamped supported beam,free supported beam.Finally the generalized finite integral transformation method is obtained for the boundary conditions of four simply edges,four clamped edges,two simply and two clamped edges.(2)The analytic solution of buckling problem of thin plate under the boundary condition of two clamped supported edges is derived,which includes the pure shear force,the one-way uniform pressure and the two-way uniform pressure.Finally the analytical solutions of critical loads in each case are obtained respectively,and the critical load values under different length and width ratios are given.(3)The analytic solution of free vibration problem of the thin plate with four clamped supported edges is solved while the analytic solution of different frequency coefficients is obtained.Compared with the numerical solution provided in the literature,error is not greater than 0.35%.(4)In order to verify the correctness of the method in this paper,the numerical solution of the elastic rectangular thin plate with four clamped supported edges under the action of pure shear force and the one-way uniform pressure.And the result of the analytical solution are compared with the result of the numerical solution by means of the finite element method,and the error is not more than 0.9%.