Generalized Displacement Solution For Elastic Stability Of Thin Rectangula Plates And Its Application

In this paper, the generalized supported edge and the rectangular plates with generalized supported edge for elastic stability are introduced. The reciprocal method is applied to establish the generalized displacement solution for the elastic stability of thin rectangular plates, and the boundary values of it are also worked out.The generalized displacement solution almost included all the solutions of the problem of elastic stability for rectangular plates with different boundary condition under uniform distributed in-plane forces. According to the boundary condition of the actual rectangular plates, it is very easy to get the characteristic equation for the problem through the boundary value of the generalized solution. This method is simple and clear, and by it, the complicated solutions for the problems of elastic stability are simplified.As application of generalized displacement solution, many problems of stability for rectangular plates are worked out, and the characteristic equation is given by it. The result can be?a reference for engineering. By calculation, it is proved that the solution is not only suited to some rectangular plates with simple boundary condition, but also suited to the rectangular plates with complicated boundary condition. So, the generalizability of the generalized solution is proved.And this solution is basis to make the usual program for the problem of elastic stability for thin rectangular plates.