Galerkin approximations to static and dynamic localization problems

A new Galerkin-type procedure is established which, unlike the classical approach, does not rely on the ®nal shape being composed of linearly independent modes. The procedure is applied to the evolution of a localized buckle of a thin elastic strip within a visco-elastic medium. Unlike the related elastic problem, no clear-cut linear eigenvalues exist to model wavelength and exponential growth/decay in the tails of the buckle pattern. The new procedure introduces variables to measure these e€ects, and allows them to change in time. This results in a more natural evolutionary process than with ®xed mode shapes. Analysis is run within an algebraic manipulator (MAPLE) and checked against that of a numerical boundary-value solver (COLPAR). # 2000 Elsevier Science Ltd. All rights reserved.