New hybrid-Trefftz Mindlin–Reissner plate elements for efficiently modeling the edge zones near free/SS1 edges

Yan Shang (State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China)
Song Cen (School of Aerospace Engineering, Tsinghua University, Beijing, China)
Wengen Ouyan (The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, Israel)

Engineering Computations

ISSN: 0264-4401

Publication date: 5 March 2018



The purpose of this paper is to propose a new finite element method (FEM) solving strategy for efficient analysis of the challenging edge effect problem in plate structures. Its main ideas are to develop special-purpose plate element models to effectively simulate the behaviors in the plate’s edge zones near free/SS1 edges.


These new elements are developed based on the hybrid-Trefftz element method. During their construction procedures, the analytical solutions of the edge effect problem, which are in exponential forms, are used to enhance the interior displacement fields. Besides, the Lagrangian multipliers are introduced into the modified hybrid-Trefftz functional for considering the stress resultant constraints at free/SS1 edges. Thus, these elements theoretically possess the abilities to correctly capture the very steep gradients of the resultant distributions in the boundary layers.


These new specialized hybrid-Trefftz plate elements can very efficiently solve the edge effect problem with high accuracy, even when distorted meshes are used. Moreover, because these elements’ construction procedures contain only boundary integrals, the computation expense for accurately integrating the exponential trial functions can be considerably saved.


This work presents an alternative novel idea for using the FEM to more effectively handle the local stress problems by incorporating the use of the analytical trial functions.



The authors would like to thank for the financial supports from the National Natural Science Foundation of China (11702133, 11272181), the Natural Science Foundation of Jiangsu Province (grant no BK20170772) and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.


Shang, Y., Cen, S. and Ouyan, W. (2018), "New hybrid-Trefftz Mindlin–Reissner plate elements for efficiently modeling the edge zones near free/SS1 edges", Engineering Computations, Vol. 35 No. 1, pp. 136-156.

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