Finite-Element Modeling of Thin-Shell Equations One of the main focus areas of our research is the modeling of the mechanical behavior of thin flexible structures. Such structures are ubiquitous in engineering design and of major importance, for example, in the automobile and aerospace industries. The mechanical behavior of thin flexible structures can be described by a fourth order PDE whose weak form takes the metric and curvature tensors of a surface in the undeformed, respectively deformed configuration into account. This treatment is based on classical Kirchhoff-Love theories taking the thin limit of such structures. Because the governing equations involve curvatures as their highest order terms any finite element treatment must work with shape functions which possess square integrable curvatures (as subdivision surfaces do; see ). Building robust finite element solvers for this problem has long been an outstanding issue in the mechanical engineering research community. We have been able to demonstrate FEM solvers for thin-shells based on subdivision surfaces. They are exceedingly robust and exhibit high accuracy. One of the main features of our approach is the unification of surface representations for geometric modeling with those used for the FEM method. Consequently the usual step of having to mesh an existing geometry is entirely avoided. This removes many of the headaches associated with simulation based engineering design since meshing methods are notoriously fragile and the results of a simulation are difficult to feedback to the original geometry. Using the same representation for geometry and finite element treatments greatly simplifies and accelerates the design cycle. To learn more see Subdivision Surfaces: A New Paradigm for Thin-Shell Finite Element Analysis or Fully C1- Conforming Elements for Finite Deformation Thin-Shell Analysis [Home]