A mixed element based on Lagrange multiplier method for modified couple stress theory

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A 2D mixed element is proposed for the modified couple stress theory. The C-1 continuity for the displacement field is required because of the second derivatives of displacement in the energy form of the theory. The C-1 continuity is satisfied in a weak sense with the Lagrange multiplier method. Asupplementary rotation is introduced as an independent variable and the kinematic relation between the physical rotation and the supplementary rotation is constrained with Lagrange multipliers. Convergence criteria and a stability condition are derived, and the number and the positions of nodes for each independent variable are determined. Internal degrees of freedom are condensed out, so the element has only 21 degrees of freedom. The proposed element passes the C0-1 patch test. Numerical results show that the principle of limitation is applied to the element and the element is robust to mesh distortion. Furthermore, the size effects are captured well with the element.
Publisher
SPRINGER
Issue Date
2017-01
Language
English
Article Type
Article
Keywords

STRAIN-GRADIENT ELASTICITY; FINITE-ELEMENT; LENGTH SCALE; PLASTICITY; FORMULATIONS; MODEL

Citation

COMPUTATIONAL MECHANICS, v.59, no.1, pp.117 - 128

ISSN
0178-7675
DOI
10.1007/s00466-016-1338-3
URI
http://hdl.handle.net/10203/223068
Appears in Collection
ME-Journal Papers(저널논문)
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