Nonlinear Analysis Method for Circular Plates

A discrete variable method is presented for the large deflection analysis of inelastic circular plates. Formulation of a problem is accomplished through a discrete lumped-parameter model of a plate on the basis of fundamental principles of mechanics. This leads consistently to a system of nonlinear centered finite-difference equations. The equations are converted to an equivalent incremental form and their solution is accomplished by an iteration technique wherein calculations are performed recursively. Certain questions concerning continuity of displacements, stiffness matrix conditioning, and stability are treated. The reliability of the method is verified through a number of favorable comparisons with other theoretical solutions as well as with available experimental results. The convergence of solutions obtained with decreasing mesh size is also well illustrated. The method is well-suited and easily programmed for high-speed digital calculations.