Lecture 18 : Wrinkling of a thin sheet under uni-axial flexible strain
In addition to this, there is a fictitious transverse force which causes the wrinkles to appear. This unknown transverse force is per unit length along direction which causes extension , where is the imposed compressive transverse displacement. Then the work done by this force is
(18.4)
Hence, total energy is written as
(18.5)
Minimization of the total energy with respect to out of place displacement yields Euler-Lagrange equation
per unit length along 
direction which causes extension 
, where 
is the imposed compressive transverse displacement. Then the work done by this force is 
yields Euler-Lagrange equation 
