An enhanced co-rotational approach for large displacement analysis of plates

This paper presents a new co-rotational approach for the large displacement analysis of plates employing 4-noded quadrilateral flat shell elements. The proposed approach benefits from (i) a simple local co-rotational system invariant to the element nodal ordering, (ii) the choice of the two smallest components of the nodal normal vector as global rotational degrees of freedom, and (iii) the use of hierarchic freedoms, that are unaffected by the co-rotational transformations, for higher-order accuracy. Important additional benefits that arise from the aforementioned features include symmetry of the tangent stiffness matrix and complete insensitivity of the large displacement transformations to the size of the incremental step. The applicability of the new approach to moderately thick as well as thin plates is illustrated by considering two alternative local formulations based on the Reissner–Mindlin and discrete Kirchhoff hypotheses. Several examples are finally presented which demonstrate the accuracy, step-insensitivity and computational benefits of the proposed co-rotational approach for large displacement analysis of plate structures