Shell Elements

Since the degenerated continuum shell element formulation was introduced by Ahmad et al. 1, it has become dominant in commercial Finite Element codes due to its advantage of being independent of any particular shell theory, versatile and cost effective, and applicable in a reliable manner to both thin and thick shells.

In the standard 4-node shell element, full integration and reduced integration schemes have been used to compute the stiffness matrices and force vectors:
  • The full integration scheme is often used in programs for static or dynamic problems with implicit time integration. It presents no problem for stability, but sometimes involves "locking" and computations are often more expensive.
  • The reduced integration scheme, especially with one-point quadrature (in the mid-surface), is widely used in programs with explicit time integration such as Radioss and other programs applied essentially in crashworthiness studies. These elements dramatically decrease the computation time, and are very competitive if the hourglass modes (which result from the reduced integration scheme) are "well" stabilized.
1 Ahmad S., Irons B.M., and Zienkiewicz O.C., “Analysis of thick and thin shell structures by curved finite elements”, Computer Methods in Applied Mechanics and Engineering, 2:419-451, 1970.