Shape ‐free arbitrary polygonal hybrid stress/displacement‐function flat shell element for linear and geometrically nonlinear analyses

In this paper, an improved flat triangular shell element is proposed. This element has three nodes, and in each node, six degrees of freedom are considered. Since there are three rotational degrees of freedom at each node, the drilling effect can be incorporated in authors' formulation. A new procedure is also suggested for updating the director vectors about which the rotational degrees of freedom are defined. In order to study large displacements and rotations, Total Lagrangian principles are employed. In addition, updating the rotational degrees of freedom is implemented using enriched updated director vectors, which are formulated based on the finite rotation method. On the other hand, small strains are considered in this formulation. By utilizing MITC method, shear and membrane locking is mitigated from new element. To examine the performance, the element passes three basic tests, including isotropy, and patch test. Moreover, a convergence study is also implemented to show the elemental behavior. Several popular benchmarks are considered to illustrate the accuracy and capability of the suggested element in geometrically nonlinear analyses.

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Geometrically nonlinear analysis of shells by quadrilateral flat shell element with drill, shear, and warping

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.5261 ◽

2016 ◽

Vol 108 (10) ◽

pp. 1248-1272 ◽

Cited By ~ 13

Author(s):

Yi Qun Tang ◽

Zhi Hua Zhou ◽

Siu Lai Chan

Keyword(s):

Nonlinear Analysis ◽

Shell Element ◽

Geometrically Nonlinear ◽

Geometrically Nonlinear Analysis ◽

Flat Shell ◽

Flat Shell Element

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

Engineering Computations ◽

10.1108/ec-04-2015-0102 ◽

2016 ◽

Vol 33 (3) ◽

Cited By ~ 8

Author(s):

Yan Shang ◽

Song Cen ◽

Chenfeng Li

Keyword(s):

Design Methodology ◽

Degrees Of Freedom ◽

A Priori ◽

Shell Element ◽

Displacement Function ◽

Plate Bending ◽

Flat Shell ◽

Flat Shell Element ◽

Plane Membrane ◽

Low Order

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-P4-11β (Cen et al. 2014) and a shape-free quadrilateral hybrid stress-function (HSF) plane membrane element HSF-Q4θ-7β (Cen et al. 2011b) with drilling degrees of freedom, a new 4-node, 24-DOF (6 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.

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