A finite element formulation based on the theory of a Cosserat point

Abstract

The theory of Cosserat points is the basis of a 3D finite element formulation allowing for large deformations in structural mechanics, that recently was presented by [1]. First attempts have revealed, that this formulation is free of showing undesired locking or hourglassing‐phenomena. It additionally shows excellent behaviour for any type of incompressible material, for large deformations and sensitive structures such as plates or shells. Within the theory of Cosserat points, the position vectors X and x, are described through director vectorsDi and di by use of trilinear shape functions Ni for an 8‐node brick element.The special choice of shape functions Ni allows for director vectors with which the deformation can be split into a homogeneous and an inhomogeneous part. This split enables the use of stiffnesses that correspond to different deformation modes. Analytical solutions to the inhomogeneous deformation modes are incorporated in the formulation and avoid the undesired phenomena. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)