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Generalized conforming Trefftz element for size-dependent analysis of thin microplates based on the modified couple stress theory

Yan Shang, Yu-Hao Mao, Song Cen, Chenfeng Li Orcid Logo

Engineering Analysis with Boundary Elements, Volume: 125, Pages: 46 - 58

Swansea University Author: Chenfeng Li Orcid Logo

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Abstract

In this work, a new displacement-based Trefftz plate element is developed for size-dependent bending analysis of the thin plate structures in the context of the modified couple stress theory. This is achieved via two steps. First, the Trefftz functions, that are derived by introducing the thin plate...

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Published in: Engineering Analysis with Boundary Elements
ISSN: 0955-7997
Published: Elsevier BV 2021
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa56142
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Abstract: In this work, a new displacement-based Trefftz plate element is developed for size-dependent bending analysis of the thin plate structures in the context of the modified couple stress theory. This is achieved via two steps. First, the Trefftz functions, that are derived by introducing the thin plate bending assumptions into the three-dimensional governing equations of the modified couple stress elasticity, are adopted as the basis functions for designing the element's displacement interpolations. Second, the generalized conforming theory is employed to meet the interelement compatibility requirements in weak sense for ensuring the convergence property. The resulting 4-node displacement-based plate element performs like nonconforming models on coarse meshes and gradually converges into a conforming one with the mesh refinement. Numerical tests reveal that the new element can efficiently capture the size-dependent mechanical responses of thin microplates and exhibits satisfactory numerical accuracy and distortion tolerance. Moreover, as the element has only three degrees of freedom (DOF) per node, it can be easily incorporated into the commonly available finite element programs.
Keywords: Trefftz finite element, Thin plate, Generalized conforming theory, Size effect, Modified couple stress theory
College: College of Engineering
Start Page: 46
End Page: 58