# One-Dimensional Finite Rotation Shell Problems in Displacement Formulation

• L.-P. Nolte
Conference paper
Part of the Lecture Notes in Engineering book series (LNENG, volume 19)

## Abstract

The present report deals with certain consequences for the displacement formulation of nonlinear first approximation shell theories if shell problems are concerned in which the partial differential equations reduce to ordinary ones. In these cases a necessary geometrical constraint is that the reference middle surface admit one-dimensional strain fields. Accordingly the shell strains, depending on differences of the metric and curvature tensors in the deformed and undeformed configuration are functions of one independent variable only. It has been shown by Simmonds [1] that then during the deformation process the shell middle surface must be a general helicoid, which additionally implies special boundary conditions, material properties and type of loadings. There are several reasons for the analysis of one-dimensional reduced shell problems. By that general nonlinear shell equations remain rather complicated and require approximate solutions by using large computer codes such that the associated one-dimensional equations may considerably reduce the cost and/or time of the nonlinear solution. Besides, the derivation of general and simplified one-dimensional shell theories gains a good insight into similar investigations of the general theory of shells.

## Keywords

Shell Theory Middle Surface Axisymmetric Deformation Displacement Formulation Finite Rotation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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