ABSTRACT
This chapter discusses the construction of numerical methods based upon efficient and robust finite elements. Finite element schemes for shell problems suffer from so-called membrane locking, that is, the finite element approximation of the membrane component of the energy is unstable with respect to the shell thickness. The most common approaches proposed to overcome the locking effect are: the use of standard displacement formulation with high-order finite elements; modified variational forms; techniques of reduced or selectively reduced integration. The chapter considers a displacement formulation solved with Serendipity finite elements of hierarchic type, with both full and reduced integration. It explores a mixed formulation introducing nonstandard finite elements, suitable for numerical solution with both uniform and distorted decompositions. To analyze the behavior of the finite elements with respect to membrane and shear locking, the chapter also considers some benchmark problems often used to assess the performance of numerical approximations.
