Axisymmetric Finite Deflection of Circular Plates

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Abstract
The axisymmetric finite deflection of circular disks and annular plates is examined. The investigation has two objectives. One is to develop a numerical technique which can be used to solve some nonlinear boundary value problems. The other objective is to obtain information on the deflection and stress distribution of circular plates which have large deflection. The nonlinear equations of equilibrium and boundary conditions are derived by the variational method. These equations are expanded into finite difference equations, and solved by a modified iteration technique. In this modified iteration technique, the loading is increased by small increments. The solution of each loading step is predicted by extrapolating the solutions of previous loading steps. The calculation is manipulated in such a fashion that the solution converges very rapidly. Numerical results of various loading conditions and boundary conditions are obtained. In all these calculations, the proposed iteration method was found to be very effective. The solution for circular plates fixed at the boundary, and subjected to uniform pressure, is in excellent agreement with the existing solution.

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