Jj. Cao, COMPUTER-EXTENDED PERTURBATION SOLUTION FOR THE LARGE DEFLECTION OF ACIRCULAR PLATE .1. UNIFORM LOADING WITH CLAMPED EDGE, Quarterly Journal of Mechanics and Applied Mathematics, 49, 1996, pp. 163-178
The idea of extending a regular perturbation series to high order by c
omputer was borrowed from physicists by fluid mechanicians. Here it is
applied for the first time to solid mechanics. Von Karman's nonlinear
plate equations are solved for uniform loading of a circular plate by
expanding in powers of the maximum deflection to 110 terms. Analysis
of the load-deflection series shows that convergence is limited by a n
on-physical square-root singularity. Mapping it away to infinity exten
ds the range of convergence to infinity, and it is then possible to ex
tract the asymptotic solution for extreme deflection, which agrees wit
h the membrane solution.