Pure plate bending in couple stress theories

Ali R. Hadjesfandiari; Arezoo Hajesfandiari; Gary F. Dargush

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arXiv · 1606.02954

Pure plate bending in couple stress theories

Ali R. Hadjesfandiari·Arezoo Hajesfandiari·Gary F. Dargush

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Abstract

In this paper, we examine the pure bending of plates within the framework of modified couple stress theory (M-CST) and consistent couple stress theory (C-CST). In this development, it is demonstrated that M-CST does not describe pure bending of a plate properly. Particularly, M-CST predicts no couple-stresses and no size effect for the pure bending of the plate into a spherical shell. This contradicts our expectation that couple stress theory should predict some size effect for such a deformation pattern. Therefore, this result clearly demonstrates another inconsistency of indeterminate symmetric modified couple stress theory (M-CST), which is based on considering the symmetric torsion tensor as the curvature tensor. On the other hand, the fully determinate skew-symmetric consistent couple stress theory (C-CST) predicts results for pure plate bending that tend to agree with mechanics intuition and experimental evidence. Particularly, C-CST predicts couple-stresses and size effects for the pure bending of the plate into a spherical shell, which represents an additional illustration of its consistency.

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Ali R. Hadjesfandiari, Arezoo Hajesfandiari, Gary F. Dargush. 2016-06-01. Pure plate bending in couple stress theories. https://arxiv.org/abs/1606.02954

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