SHELL THEORY VERSUS DEGENERATION - A COMPARISON IN LARGE ROTATION FINITE-ELEMENT ANALYSIS

The first part of this study addresses the controversy 'degenerated solid approach' versus 'shell theory'. It is shown that both formulations differ only in the kind of discretization if they are based on the same mechanical assumptions. In particular for degenerated shell elements different versions of explicit integration across the thickness are discussed. Among these are the approximation 'Jacobian across the thickness is constant', proven to be too restrictive, and the series expansion of the inverse Jacobian which turns out to be unnecessary although it leads to equations of the same order as those of a 'best first approximation' of a shell theory. The second part deals with the description of large rotations. It is demonstrated for problems formulated in three components of a rotation vector that a straightforward derivation results in a symmetric tangent stiffness matrix. However, a modified version is also added leading to an unsymmetric matrix already discussed in the literature. For shell problems with only two rotational variables both formulations coincide.