The Cosserat surface as a shell model, theory and finite-element formulation

Relying on the concept of a Cosserat continuum, the reduction of the three-dimensional equations of a shell body to two-dimensions is carried out in a direct manner by considering the Cosserat continuum to be a two-dimensional surface. By that, a non-linear shell theory, including transverse shear strains, with exact description of the kinematical fields is derived. The strain measures are taken to be the first and the second Cosserat deformation tensors allowing for an explicit use of a three parametric rotation tensor. Thus, inplane rotations, also called drilling degrees of freedom, are included in a natural way. The structure of the configuration space is discussed and two possible definitions of it are given equipped once with a Killing metric and once with an Euclidean one. A partially mixed variational principle is proposed on the base of which an efficient hybrid finite-element formulation, which does not exhibit locking phenomena, is developed. Various numerical examples of shell deformations at finite rotations, with excellent element performance, are presented.

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