A large-strain elasto-plastic shell formulation using the Morley triangle

The paper describes a large-strain elasto–plastic formulation for shells, which is based on the faceted ‘Morley triangle’, with rotation variables only being provided at each mid-side in the form of a rotation about the side. A co-rotational formulation is adopted, with the local deformation gradient being obtained from a polar decomposition using F=RU. The material description is then based around ‘loge U’, with U being decomposed into principal directions. Plasticity is treated with the aid of the multiplicative F=FeFp. In contrast to many earlier formulations with the Morley triangle, the current formulation is invariant to the node numbering. In order to achieve this invariance, it is necessary to re-visit the origins of the Morley triangle and to re-cast the formulation as a special form of ‘discrete- Kirchho> approach’. The associated constraint is now applied in relation to the ‘current con4guration