The asymptotic limit of an eigenvalue problem related to the buckling of rolled elastic strips

摘要: We examine the structure of marginal stability curves an eigenvalue problem related to buckling deformations observed during cold rolling sheet metal. The instability in question is characterised by a centre “wave” pattern and arises as interplay between self-equilibrating residual stresses associated with process, on one hand, traction force acting strip, other. When latter effect dominates, we show that singular perturbation methods can be used unravel number novel mathematical features linear bifurcation equation. also provide simple quantitative formulae facilitate easy interpretation corresponding physical phenomena.