Large Deflection And Post-buckling Of Rectangular Thin Plates With Variable Thickness

Variable thickness plate is widely used in various engineering practices because of its light weight and uneven distribution of stress and strain.Many of the concrete slabs used in civil engineering such as building construction,bridges and roads,and high-precision plates used in aviation and mechanical fields are in the form of variable thickness.With the development of engineering technology,the requirement of plate displacement control is higher and higher,and the accuracy of plate deformation is higher and higher.It is no longer applicable to calculate the deflection of variable thickness plate approximately through the deflection theory of equal thickness plate.In this paper,the bending theory model of rectangular thin plate with variable thickness is established,and a new numerical method is proposed.The nonlinear large deflection and post-buckling of thin plates are studied by the proposed method.The details are as follows:1.The nonlinear equilibrium differential equation and strain compatibility equation of rectangular thin plate with variable thickness and simply supported on four sides under transverse uniform load are established,and the deflection of thin plate is obtained by Galerkin method and iterative method.The results show that the maximum deflection point of the thin plate is shifted from the center point to the side with small thickness.The distribution of deflection along the direction of thickness variation is asymmetric to the bisector of the plate surface,while the distribution along the direction of constant thickness is symmetric to the bisector of the plate surface.2.The deflection and internal force of anisotropic rectangular plates with variable thickness are calculated by Galerkin iterative method,and the results are compared with those of plates with equal thickness.3.The energy method is used to establish the strain energy equation of rectangular thin plate with variable thickness and simply supported on four sides under the action of longitudinal uniform load.The displacement of thin plate is taken as the series form of double trigonometric function,and the displacement of thin plate is obtained by Ritz method and iterative method.4.Taking the deflection as the perturbation parameter,the governing equation of the post-buckling problem of the simply supported rectangular thin plate with variable thickness and initial imperfections is solved by using the quadratic perturbation method,and the mathematical expression of the load displacement relationship of the thin plate is obtained.