An optimally constrained 4 node quadrilateral thin plate bending element

Abstract

Recent advances in the study of optimal integration of quadrilateral plate bending elements based on Mindlin's plate theory points to a four-noded quadrilateral plate bending element which can be based on thin-plate theory. This isoparametric element uses independent bi-linear interpolations for the transverse displacement W and face rotations θ_x and θ_y. An optimal set of Kirchhoff constraints are enforced at the centre of the element by a penalty function type formulation. The choice of the number of constraints and the effect of grid-orientation and grid-distortion with regard to this is studied in detail.