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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 فرستنده : bluesky iopscienceb8b93028-2cfc-20160324114637.pdf