Abstract
Shortwavelength wrinkles that appear on an initially stretched thin elastic plate under transverse loading are examined. As the degree of loading is increased, wrinkles appear and their structure at the onset of buckling takes on one of three distinct forms depending on the size of the imposed stretching. With relatively little stretching, the wrinkles sit off the rim of the plate at a location which is not known a priori, but which is determined via a set of consistency conditions. These take the form of constraints on the solutions of certain coupled nonlinear differential equations that are solved numerically. As the degree of stretching grows, an asymptotic solution of the consistency conditions is possible, which heralds the structure that governs a second regime. Now the wrinkle sits next to the rim, where its detailed structure can be described by the solution of suitably scaled Airy equations. In each of these first two regimes the F opplvon K arman bifurcation equations remain coupled, but as the initial stretching becomes stronger the governing equations separate. Further use of singular perturbation arguments allows us to identify the wavelength wrinkle which is likely to be preferred in practice.
Original language  English 

Pages (fromto)  10091029 
Number of pages  21 
Journal  SIAM Journal on Applied Mathematics 
Volume  78 
Issue number  2 
DOIs  
Publication status  Published  29 Mar 2018 
Externally published  Yes 
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Ciprian Coman
 Department of Computer Science  Senior Lecturer in Mathematics
 School of Computing and Engineering
 Centre for Mathematics and Data Science  Member
 Centre for Autonomous and Intelligent Systems  Member
Person: Academic