Nonlinear shell theory with finite rotations and finite strains: recent achievements

We discuss a theoretical formulation of a fully nonlinear shell model, capable of representing finite rotations and finite strains. The latter imposes that one should account for through-the-thickness stretching, which allows for direct use of 3d constitutive equations from classical continuum model. Three different possibilities for implementing this kind of shell model within the framework of the finite element method are examined, the first one leading to 7 nodal parameters and the remaining two to 6 nodal parameters. The 7-parameter shell model with no simplification of kinematic terms is compared to the 7-parameter shell model which exploits usual simplifications of the Green-Lagrange strains. Two different ways of implementing the incompatible mode method for reducing the number of parameters to 6 are presented. One implementation uses an additive decomposition of the strains and the other an additive decomposition of the deformation gradient. A couple of numerical examples are given to illustrate performance of the shell elements developed herein.