A non-conforming plate facet-shell finite element with drilling stiffness

When a facet-shell finite element is used to represent a three-dimensional geometry, an incomplete connection of the rotations between adjacent finite elements may occur. In fact, the in-plane rotations from one finite element may not assemble correctly to the rotation degrees-of-freedom of an adjacent finite element, simply because there is a missing rotation degree-of-freedom, the out-plane rotation. To avoid this difficulty, the facet-shell formulation must provide a complete description of the nodal translation and rotation fields, allowing the definition of the six spatial degrees-of-freedom for each node of the finite element. Despite the huge interest on providing a solution for this issue, which is demonstrated by the sporadic but remarkable studies on the subject published by renowned researchers in the field, there is still a lack in valuable, accurate and cost effective solutions, especially for quadrilateral finite elements. In this study a non-conforming quadrilateral facet-shell finite element, providing a complete degrees-of-freedom field, is formulated and analyzed. The assessment of the proposed finite element is performed by comparing the numerical results from a set of usually applied benchmark problems with those obtained from classic and up-to-date finite elements with drilling stiffness and a similar finite element without out-plane rotation. The proposed finite element is capable to model planar and non-planar structures, and the numerical results achieved with its application onto several case studies proved its accuracy and the ability to describe the complete displacement field.