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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 by John Wiley & Sons, Ltd.

Compressed sandwich structures, comprising two stiff face plates separated by a softer core material, while designed principally as efficient integral structures, can lose this quality when faces buckle locally. Interaction between overall (Euler) buckling and local buckling of one face suggests that failure will localize into the centre. A variational formulation, leading to a pair of nonlinear differential equations subject to integral constraints, describes the post-buckling response. These are solved by a combination of numerical shooting and continuation techniques, such that the response far into the unstable post-buckling regime can be portrayed. Solutions with both linear and nonlinear constitutive core relations are compared with the results of an engineering (body-force) approach, and with those of earlier (periodic) Rayleigh-Ritz analyses. The latter demonstrate the extra destabilization that comes with localization.