On the Derivation and Efficient Computation of Large Rotation Shell Models

Within the past few years remarkable progress has been achieved on the nonlinear analysis of so termed flexible shells, mainly influenced by the fundamental results of Reissner, John and Koiter [1–4]. A novel approach to the displacement formulation of general and constrained geometrically nonlinear shell equations has been given in recent years by Pietraszkiewicz [5–7]. In particular, based on polar decomposition of shell strains and rotations it was suggested to classify small strain shell models according to the magnitude of the rotation angle of the material elements. It is known from the literature that most of the engineering shell problems may be tackled accurately enough with the help of moderate rotation shell theories [5–12]. Numerical applications of corresponding shell equations may be found e.g. in [12–14], There are, however, various one- and two-dimensional shell problems to which large rotation shell models with nonlinear membran and bending strains should be applied. In these situations the rotational part of deformation dominates. Several shell theories with nonlinear change of curvature expressions have been already given (see [15–17] and literature cited therein). It turned out, however, that most of the corresponding field equations are very complicated and virtually useless for numerical applications. On the other hand we have shown recently [16] that various approaches used in engineering practice may lead to inconsistent shell equations.