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Distortion-resistant and locking-free eight-node elements effectively capturing the edge effects of Mindlin–Reissner plates

Yi Bao (Department of Engineering Mechanics, Tsinghua University, Beijing, China)
Song Cen (Department of Engineering Mechanics, Tsinghua University, Beijing, China and High Performance Computing Center, Tsinghua University, Beijing, China and Key Laboratory of Applied Mechanics, Tsinghua University, Beijing, China)
Chenfeng Li (Zienkiewicz Centre for Computational Engineering, Energy Safety Research Institute, Swansea University, Swansea, UK)

Engineering Computations

ISSN: 0264-4401

Article publication date: 18 April 2017




A simple shape-free high-order hybrid displacement function element method is presented for precise bending analyses of Mindlin–Reissner plates. Three distortion-resistant and locking-free eight-node plate elements are proposed by utilizing this method.


This method is based on the principle of minimum complementary energy, in which the trial functions for resultant fields are derived from two displacement functions, F and f, and satisfy all governing equations. Meanwhile, the element boundary displacements are determined by the locking-free arbitrary order Timoshenko’s beam functions. Then, three locking-free eight-node, 24-DOF quadrilateral plate-bending elements are formulated: HDF-P8-23β for general cases, HDF-P8-SS1 for edge effects along soft simply supported (SS1) boundary and HDF-P8-FREE for edge effects along free boundary.


The proposed elements can pass all patch tests, exhibit excellent convergence and possess superior precision when compared to all other existing eight-node models, and can still provide good and stable results even when extremely coarse and distorted meshes are used. They can also effectively solve the edge effect by accurately capturing the peak value and the dramatical variations of resultants near the SS1 and free boundaries. The proposed eight-node models possess potential in engineering applications and can be easily integrated into commercial software.


This work presents a new scheme, which can take the advantages of both analytical and discrete methods, to develop high-order mesh distortion-resistant Mindlin–Reissner plate-bending elements.



This work is financially supported by the National Natural Science Foundation of China (11272181), the Specialized Research Fund for the Doctoral Program of Higher Education of China (20120002110080) and the Tsinghua University Initiative Scientific Research Program (2014z09099).


Bao, Y., Cen, S. and Li, C. (2017), "Distortion-resistant and locking-free eight-node elements effectively capturing the edge effects of Mindlin–Reissner plates", Engineering Computations, Vol. 34 No. 2, pp. 548-586.



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