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-P4-11 beta (Cen et al., 2014) and a shape-free quadrilateral hybrid stress-function (HSF) plane membrane element HSF-Q4 theta-7 beta (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 correction strategy (Taylor, 1987) is also employed. Findings - The element stiffness matrix of a new simple 4-node, 24-DOF quadrilateral flat shell element is obtained. The resulting models, denoted as HDF-SH4, not only possesses all advantages of original HDF plate and HSF plane elements when analyzing plate and plane structures, but also exhibits good performances for analyses of complicated spatial shell structures. Especially, it is quite insensitive to mesh distortions. Originality/value - This work presents a new scheme, which can take the advantages of both analytical and discrete methods, to develop low-order mesh-distortion resistant flat shell elements.