A 4-node quadrilateral flat shell element formulated by the shape-free HDF plate and HSF membrane elements

Purpose – The purpose of this paper is to propose an efficient low-order quadrilateral flat shell element that possesses all outstanding advantages of novel shape-free plate bending and plane membrane elements proposed recently. Design/methodology/approach – By assembling a shape-free quadrilateral hybrid displacement-function (HDF) plate bending element HDF-P4-11s (Cen et al., 2014) and a shape-free quadrilateral hybrid stress-function (HSF) plane membrane element HSF-Q4-7s (Cen et al., 2011b) with drilling degrees of freedom (DOF), a new 4-node, 24-DOF (six DOFs per node) quadrilateral flat shell element is successfully constructed. The trial functions for resultant/stress fields within the element are derived from the analytical solutions of displacement and stress functions for plate bending and plane problems, respectively, so that they can a priori satisfy the related governing equations. Furthermore, in order to take the influences of moderately warping geometry into consideration, the rigid link c...

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