Bernoulli–Euler beam model based on a modified couple stress theory

A new model for the bending of a Bernoulli-Euler beam is developed using a modified couple stress theory. A variational formulation based on the principle of minimum total potential energy is employed. The new model contains an internal material length scale parameter and can capture the size effect...

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Bibliographic Details
Published in:Journal of micromechanics and microengineering 2006-11, Vol.16 (11), p.2355-2359
Main Authors: Park, S K, Gao, X-L
Format: Article
Language:English
Subjects:
Applied sciences
Electronics
Exact sciences and technology
Instruments, apparatus, components and techniques common to several branches of physics and astronomy
Mechanical engineering. Machine design
Mechanical instruments, equipment and techniques
Microelectronic fabrication (materials and surfaces technology)
Micromechanical devices and systems
Physics
Precision engineering, watch making
Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices
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Summary:A new model for the bending of a Bernoulli-Euler beam is developed using a modified couple stress theory. A variational formulation based on the principle of minimum total potential energy is employed. The new model contains an internal material length scale parameter and can capture the size effect, unlike the classical Bernoulli-Euler beam model. The former reduces to the latter in the absence of the material length scale parameter. As a direct application of the new model, a cantilever beam problem is solved. It is found that the bending rigidity of the cantilever beam predicted by the newly developed model is larger than that predicted by the classical beam model. The difference between the deflections predicted by the two models is very significant when the beam thickness is small, but is diminishing with the increase of the beam thickness. A comparison shows that the predicted size effect agrees fairly well with that observed experimentally.
ISSN:0960-1317
1361-6439
DOI:10.1088/0960-1317/16/11/015