A new bernoulli-euler beam model based on a modified couple stress theory

S. K. PARK; X.-L. GAO

doi:10.1061/40830(188)166

A new bernoulli-euler beam model based on a modified couple stress theory

S. K. PARK, X.-L. GAO^*

^*Corresponding author for this work

Research output: Book Chapters | Papers in Conference Proceedings › Conference paper (refereed) › Research › peer-review

5 Citations (Scopus)

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 total minimum potential energy principle is employed. The new model contains an internal material length parameter and can capture the size effect, unlike the classical Bernoulli-Euler beam model. The former reduces to the latter when the material length parameter is set to zero. As a direct application of the new model, a cantilever beam problem is solved. It is found that the rigidity of the cantilever beam predicted by the new 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 (below 10 μm), but is diminishing with the increase of the beam thickness. This demonstrates that the new model can indeed predict the size effect at the micron scale observed in bending tests. Copyright ASCE 2006.

Original language	English
Title of host publication	Earth and Space 2006 - Proceedings of the 10th Biennial International Conference on Engineering, Construction, and Operations in Challenging Environments
Editors	Ramesh B. MALLA, Wieslaw K. BINIENDA, Arup K. MAJI
DOIs	https://doi.org/10.1061/40830(188)166
Publication status	Published - 28 Dec 2006
Externally published	Yes
Event	The 10th Biennial International Conference on Engineering, Construction, and Operations in Challenging Environments - League City, United States Duration: 5 Mar 2006 → 8 Mar 2006

Conference

Conference	The 10th Biennial International Conference on Engineering, Construction, and Operations in Challenging Environments
Country/Territory	United States
City	League City
Period	5/03/06 → 8/03/06

Access to Document

10.1061/40830(188)166

Cite this

@inproceedings{f0555f7e97cf43d890a5efb8a2549c55,

title = "A new bernoulli-euler beam model based on a modified couple stress theory",

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 total minimum potential energy principle is employed. The new model contains an internal material length parameter and can capture the size effect, unlike the classical Bernoulli-Euler beam model. The former reduces to the latter when the material length parameter is set to zero. As a direct application of the new model, a cantilever beam problem is solved. It is found that the rigidity of the cantilever beam predicted by the new 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 (below 10 μm), but is diminishing with the increase of the beam thickness. This demonstrates that the new model can indeed predict the size effect at the micron scale observed in bending tests. Copyright ASCE 2006.",

author = "PARK, \{S. K.\} and X.-L. GAO",

year = "2006",

month = dec,

day = "28",

doi = "10.1061/40830(188)166",

language = "English",

isbn = "9780784408308",

editor = "MALLA, \{Ramesh B.\} and BINIENDA, \{Wieslaw K.\} and MAJI, \{Arup K.\}",

booktitle = "Earth and Space 2006 - Proceedings of the 10th Biennial International Conference on Engineering, Construction, and Operations in Challenging Environments",

note = "The 10th Biennial International Conference on Engineering, Construction, and Operations in Challenging Environments ; Conference date: 05-03-2006 Through 08-03-2006",

}

PARK, SK & GAO, X-L 2006, A new bernoulli-euler beam model based on a modified couple stress theory. in RB MALLA, WK BINIENDA & AK MAJI (eds), Earth and Space 2006 - Proceedings of the 10th Biennial International Conference on Engineering, Construction, and Operations in Challenging Environments. The 10th Biennial International Conference on Engineering, Construction, and Operations in Challenging Environments, League City, Texas, United States, 5/03/06. https://doi.org/10.1061/40830(188)166

A new bernoulli-euler beam model based on a modified couple stress theory. / PARK, S. K.; GAO, X.-L.
Earth and Space 2006 - Proceedings of the 10th Biennial International Conference on Engineering, Construction, and Operations in Challenging Environments. ed. / Ramesh B. MALLA; Wieslaw K. BINIENDA; Arup K. MAJI. 2006.

Research output: Book Chapters | Papers in Conference Proceedings › Conference paper (refereed) › Research › peer-review

TY - GEN

T1 - A new bernoulli-euler beam model based on a modified couple stress theory

AU - PARK, S. K.

AU - GAO, X.-L.

PY - 2006/12/28

Y1 - 2006/12/28

N2 - 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 total minimum potential energy principle is employed. The new model contains an internal material length parameter and can capture the size effect, unlike the classical Bernoulli-Euler beam model. The former reduces to the latter when the material length parameter is set to zero. As a direct application of the new model, a cantilever beam problem is solved. It is found that the rigidity of the cantilever beam predicted by the new 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 (below 10 μm), but is diminishing with the increase of the beam thickness. This demonstrates that the new model can indeed predict the size effect at the micron scale observed in bending tests. Copyright ASCE 2006.

AB - 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 total minimum potential energy principle is employed. The new model contains an internal material length parameter and can capture the size effect, unlike the classical Bernoulli-Euler beam model. The former reduces to the latter when the material length parameter is set to zero. As a direct application of the new model, a cantilever beam problem is solved. It is found that the rigidity of the cantilever beam predicted by the new 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 (below 10 μm), but is diminishing with the increase of the beam thickness. This demonstrates that the new model can indeed predict the size effect at the micron scale observed in bending tests. Copyright ASCE 2006.

UR - https://www.scopus.com/pages/publications/33845711022

U2 - 10.1061/40830(188)166

DO - 10.1061/40830(188)166

M3 - Conference paper (refereed)

AN - SCOPUS:33845711022

SN - 9780784408308

BT - Earth and Space 2006 - Proceedings of the 10th Biennial International Conference on Engineering, Construction, and Operations in Challenging Environments

A2 - MALLA, Ramesh B.

A2 - BINIENDA, Wieslaw K.

A2 - MAJI, Arup K.

T2 - The 10th Biennial International Conference on Engineering, Construction, and Operations in Challenging Environments

Y2 - 5 March 2006 through 8 March 2006

ER -

A new bernoulli-euler beam model based on a modified couple stress theory

Abstract

Conference

Access to Document

Other files and links

Fingerprint

Cite this