FINITE ELEMENT MODELLING OF SPATIALLY CHAOTIC STRUCTURES

A simple non-linear mechanical system comprising a pin-jointed string of nite-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 nite element model. At loads less than the critical buckling load, a preferred buckling con guration is found that is localized along the length. In the limit of in nite length this is described as a homoclinic connection in phase space, joining the at equilibrium state to itself. The in nite sequence of homoclinic points thus de ned embeds within the complex topological structure of a homoclinic tangle, within which also appear periodic, quasi-periodic, and chaotic spatial solutions. Implications in the nite element setting are discussed.