Determination of large deflections for elastic circular plate

Elastic large deflections of a clamped circular plate subjected to uniform normal pressure are governed by a system of ordinary nonlinear differential equations of the fifth order. The solution of the system must satisfy the given boundary conditions at the centre and the edge of the plate. An analytical solution of this boundary-value problem is not feasible. The numerical solution of the problem using the shooting method is reported in this paper. Integration of differential equations is carried out by the Runge–Kutta method. The method of embedded polygons is used to find initial values of deflections at the edge of the plate. The idea of the method is to construct a sequence of embedded polygons in Euclidean phase space that converge to a single point that maps the desired solution. Polygon vertices are determined under the assumption that each of the boundary conditions is a function of only one of the unknowns in the set of initial conditions. On the basis of this algorithm, a computer program has been developed. Numerical examples illustrate the capabilities of the program. The results of solving examples are presented in the form of graphs of distributions of deflections and stresses in the plate.