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

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

S K Park and X-L Gao
Department of Mechanical Engineering, Texas A&M University, 3123 TAMU,
College Station, TX 77843-3123, USA
E-mail: xlgao@tamu.edu
Received 4 April 2006, in final form 25 August 2006
Published 15 September 2006
Online at stacks.iop.org/JMM/16/2355
Abstract
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.

 

INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF MICROMECHANICS AND MICROENGINEERING
J. Micromech. Microeng. 16 (2006) 2355–2359 doi:10.1088/0960-1317/16/11/015

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