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Investigation of the size effects in Timoshenko beams based on the couple stress theory

Asghari, M ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1007/s00419-010-0452-5
  3. Publisher: 2011
  4. Abstract:
  5. In this paper, a size-dependent Timoshenko beam is developed on the basis of the couple stress theory. The couple stress theory is a non-classic continuum theory capable of capturing the small-scale size effects on the mechanical behavior of structures, while the classical continuum theory is unable to predict the mechanical behavior accurately when the characteristic size of structures is close to the material length scale parameter. The governing differential equations of motion are derived for the couple-stress Timoshenko beam using the principles of linear and angular momentum. Then, the general form of boundary conditions and generally valid closed-form analytical solutions are obtained for the axial deformation, bending deflection, and the rotation angle of cross sections in the static cases. As an example, the closed-form analytical results are obtained for the response of a cantilever beam subjected to a static loading with a concentrated force at its free end. The results indicate that modeling on the basis of the couple stress theory causes more stiffness than modeling by the classical beam theory. In addition, the results indicate that the differences between the results of the proposed model and those based on the classical Euler-Bernoulli and classical Timoshenko beam theories are significant when the beam thickness is comparable to its material length scale parameter
  6. Keywords:
  7. Analytical results ; Axial deformations ; Beam thickness ; Bending deflection ; Characteristic size ; Classical beam theory ; Classical continuum theory ; Closed form ; Closed-form analytical solutions ; Concentrated force ; Continuum theory ; Couple stress theory ; Cross section ; Euler-Bernoulli ; Free end ; Governing differential equations ; Material length scale ; Material length scale parameter ; Mechanical behavior ; Rotation angles ; Size effects ; Size-dependent behavior ; Static loading ; Timoshenko beam ; Timoshenko beam theory ; Bending (deformation) ; Bending (forming) ; Boundary conditions ; Continuum mechanics ; Equations of motion ; Mechanical engineering ; Particle beams ; Stresses
  8. Source: Archive of Applied Mechanics ; Volume 81, Issue 7 , July , 2011 , Pages 863-874 ; 09391533 (ISSN)
  9. URL: http://link.springer.com/article/10.1007%2Fs00419-010-0452-5