Stress resultant geometrically nonlinear shell theory with drilling rotations—Part I. A consistent formulation Original Research Article

In this work we present a consistent theoretical framework for a novel stress resultant geometrically nonlinear shell theory. The main feature of the present shell theory development, which stands in contrast with the classical developments in the shell theory, is the presence of a rotation component around the shell normal (so called drilling rotation) in the description of shell finite rotations. The relationship of the proposed theory with a finite deformation theory of a three-dimensional continuum with independent rotation field is clearly identified. The latter is shown to be an important link which facilitates the proper choice of the shell constitutive model, and a proper construction of the regularized form of the theory capable of supporting the drilling rotations. The corresponding linearized form of the present shell theory is discussed in the closure.