ISSN:
0029-5981
Schlagwort(e):
localization
;
spatial chaos
;
buckling
;
discrete system
;
mapping
;
non-linear
;
finite elements
;
homoclinic connection
;
Engineering
;
Numerical Methods and Modeling
Quelle:
Wiley InterScience Backfile Collection 1832-2000
Thema:
Mathematik
,
Technik allgemein
Notizen:
A simple non-linear mechanical system comprising a pin-jointed string of finite-length links, supported by elastic springs at the pins and compressed by an axial load, is viewed from two perspectives. When seen as an initial-value problem, equilibrium equations provide an iterative non-linear mapping. When seen as a boundary-value problem, it becomes a simple finite element model. At loads less than the critical buckling load, a preferred buckling configuration is found that is localized along the length. In the limit of infinite length this is described as a homoclinic connection in phase space, joining the flat equilibrium state to itself. The infinite sequence of homoclinic points thus defined embeds within the complex topological structure of a homoclinic tangle, within which also appear periodic, quasi-periodic, and chaotic spatial solutions. Implications in the finite element setting are discussed. © 1997 John Wiley & Sons, Ltd.
Zusätzliches Material:
15 Ill.
Materialart:
Digitale Medien
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