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8‐node hexahedral unsymmetric element with rotation degrees of freedom for modified couple stress elasticity

Yan Shang, Chenfeng Li Orcid Logo, Kang‐Yu Jia

International Journal for Numerical Methods in Engineering, Volume: 121, Issue: 12, Pages: 2683 - 2700

Swansea University Author: Chenfeng Li Orcid Logo

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DOI (Published version): 10.1002/nme.6325

Abstract

A new C0 8‐node 48‐DOF hexahedral element is developed for analysis of size‐dependent problems in the context of the modified couple stress theory by extending the methodology proposed in our recent work (Shang et al., Int J Numer Methods Eng 119(9): 807‐825, 2019) to the three‐dimensional (3D) case...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981 1097-0207
Published: Wiley 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa54099
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Abstract: A new C0 8‐node 48‐DOF hexahedral element is developed for analysis of size‐dependent problems in the context of the modified couple stress theory by extending the methodology proposed in our recent work (Shang et al., Int J Numer Methods Eng 119(9): 807‐825, 2019) to the three‐dimensional (3D) cases. There are two major innovations in the present formulation. First, the independent nodal rotation degrees of freedom (DOFs) are employed to enhance the standard 3D isoparametric interpolation for obtaining the displacement and strain test functions, as well as to approximatively design the physical rotation field for deriving the curvature test function. Second, the equilibrium stress functions instead of the analytical functions are used to formulate the stress trial function whilst the couple stress trial function is directly obtained from the curvature test function by using the constitutive relationship. Besides, the penalty function is introduced into the virtual work principle for enforcing the C1 continuity condition in weak sense. Several benchmark examples are examined and the numerical results demonstrate that the element can simulate the size‐dependent mechanical behaviors well, exhibiting satisfactory accuracy and low susceptibility to mesh distortion.
Keywords: hexahedral element, modified couple stress theory, rotation degree of freedom, size-dependent, unsymmetric FEM
College: Faculty of Science and Engineering
Issue: 12
Start Page: 2683
End Page: 2700

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