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A size-dependent beam element based on the modified couple stress theory

Kahrobaiyan, M. H ; Sharif University of Technology

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  1. Type of Document: Article
  2. Abstract:
  3. In this paper, the modified couple stress theory is employed to develop a size-dependent beam element able to predict the size-dependency observed in microbeams. The stiffness matrix is obtained for the aforementioned beam element. As an example, the deflection of a microcantilever is evaluated using the proposed beam elements and the results of the finite element method are compared to the analytical results obtained by the classical beam theory. The maximum deflection of the beam is depicted versus the ratio of the beam thickness to the material length scale parameter, the parameter appearing in non-classical continuum theories. The results show that when the characteristic size of the beam (thickness, diameter, etc) is small, like the beam used in MEMS and NEMS, the difference between the results of the current model and those obtained by the classical beam theory is significant but it diminishes as the characteristic size increases. Copyright
  4. Keywords:
  5. Analytical results ; Beam elements ; Beam thickness ; Characteristic size ; Classical beam theory ; Continuum theory ; Current models ; Material length scale ; Maximum deflection ; Micro beams ; Micro-cantilevers ; Modified couple stress theories ; Size-Dependency ; Continuum mechanics ; Finite element method ; Mechanical engineering ; Stiffness matrix ; Exhibitions
  6. Source: ASME 2011 International Mechanical Engineering Congress and Exposition, IMECE 2011, 11 November 2011 through 17 November 2011, Denver, CO ; Volume 8 , 2011 , Pages 591-597 ; 9780791854945 (ISBN)
  7. URL: http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=1644852