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The Computation Of One-Parameter Families Of Bifurcating Elastic Surfaces (1998)
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BibTeX
@MISC{Baginski98thecomputation,
author = {Frank E. Baginski},
title = {The Computation Of One-Parameter Families Of Bifurcating Elastic Surfaces},
year = {1998}
}
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Abstract
. We consider the problem of constructing the middle surface of a deformed elastic shell from its first and second fundamental forms, a fffi and b fffi . The undeformed shell is a spherical cap of radius R and thickness h with an angular width 2`0 where 0 ! `0 ! =2. The cap is subjected to a constant uniform load and is simply supported at its edge. We seek to compute the one--parameter families of buckled states which branch from the unbuckled state of the shell. This is accomplished in two steps. First, a finite element method is used to solve the governing shell equations, a pair of fourth--order nonlinear partial differential equations. A solution of this system is a curvature potential w, a stress potential f , and the load . Using Liapunov-Schmidt reduction, it can be shown that solutions possessing a variety of symmetries bifurcate from the unbuckled state of the shell. In the work that is presented here, we will numerically continue these local branches. We parametrize solut...
Keyphrases
one-parameter family bifurcating elastic surface unbuckled state middle surface deformed elastic shell undeformed shell fourth order partial differential equation parameter family second fundamental form angular width curvature potential constant uniform load spherical cap liapunov-schmidt reduction shell equation local branch stress potential finite element method
