A 10-node tetrahedral element with condensed Lagrange multipliers for the modified couple stress theory

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In this paper, a mixed tetrahedral element based on the Lagrange multiplier is newly developed for the modified couple stress theory. The limitations of the Lagrange multiplier method are that the total number of degrees of freedom is increased and that there are zeros in the diagonal term of the stiffness matrix. We developed a method to overcome the limitations by condensing out the Lagrange multipliers in the calculation of the element stiffness. Higher-order rotation modes are introduced. As condensing out the rotation modes, the Lagrange multiplier is also condensed. The total number of degrees of freedom can be greatly reduced, maximizing computational efficiency. Through numerical examples, the convergence and efficiency of the proposed elements were validated. The developed element is expected to be used for the analysis of micro/nano-scale structures. © 2020 Elsevier Ltd
Publisher
PERGAMON-ELSEVIER SCIENCE LTD
Issue Date
2021-04
Language
English
Article Type
Article
Citation

COMPUTERS & STRUCTURES, v.246, pp.106476

ISSN
0045-7949
DOI
10.1016/j.compstruc.2020.106476
URI
http://hdl.handle.net/10203/281747
Appears in Collection
ME-Journal Papers(저널논문)
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