  Numerically simulating deformations in thin elastic sheets is a challenging
problem in computational mechanics due to destabilizing compressive stresses
that result in wrinkling. Determining the location, structure, and evolution of
wrinkles in these problems have important implications in design and is an area
of increasing interest in the fields of physics and engineering. In this work,
several numerical approaches previously proposed to model equilibrium
deformations in thin elastic sheets are compared. These include standard finite
element-based static post-buckling approaches as well as a recently proposed
method based on dynamic relaxation, which are applied to the problem of an
annular sheet with opposed tractions where wrinkling is a key feature.
Numerical solutions are compared to analytic predictions, enabling a
quantitative evaluation of the predictive power of the various methods. Results
indicate that static finite element approaches are highly sensitive to initial
imperfections, relying on \textit{a priori} knowledge of the equilibrium
wrinkling pattern to generate optimal results. In contrast, dynamic relaxation
is much less sensitive to initial imperfections and can generate solutions for
a wide variety of loading conditions without requiring knowledge of the
equilibrium solution beforehand.
