On `best' shell models – From classical shells, degenerated and multi-layered concepts to 3D

Summary Problems of solid mechanics are most generally formulated within 3D continuum mechanics. However, engineering models favor reduced dimensions, in order to portray mechanical properties by surface or curvilinear approximations. Such attempts for dimensional reduction constitute interactions between theoretical formulations and numerical techniques. A classical reduced model for thin bodies is represented by shell theory, an approximation in terms of resultants and first-order moments. If the shell theory, with its inherent errors, is considered as qualitatively insufficient for a particular problem, a further improvement is given by solid shell models, which are gained by direct linear interpolation of the 3D kinematic relations. They improve considerably the analytic capabilities for shells, especially when their congenital locking effects are handled by variational `convergence tricks'. The next step towards 3D quality are layered shells or solid shell elements. The present paper compares these three approximation stages from the point of view of multi-director (integral) transformations of classical continuum mechanics. It offers physical convergence requirements for each of the treated models. Partial support to the present study by the German Science Foundation (DFG) within the Special Research Center (SFB) 398 is gratefully acknowledged.