COMPUTER-EXTENDED PERTURBATION SOLUTION FOR THE LARGE DEFLECTION OF ACIRCULAR PLATE .1. UNIFORM LOADING WITH CLAMPED EDGE

Authors
Citation
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
Citations number
20
Categorie Soggetti
Mathematical Method, Physical Science",Mathematics,Mechanics,Mathematics
ISSN journal
00335614
Volume
49
Year of publication
1996
Part
2
Pages
163 - 178
Database
ISI
SICI code
0033-5614(1996)49:<163:CPSFTL>2.0.ZU;2-0
Abstract
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.