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A nonlinear strain gradient beam formulation

Kahrobaiyan, M. H ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1016/j.ijengsci.2011.01.006
  3. Abstract:
  4. In this paper, a nonlinear size-dependent Euler-Bernoulli beam model is developed based on a strain gradient theory, capable of capturing the size effect. Considering the mid-plane stretching as the source of the nonlinearity in the beam behavior, the governing nonlinear partial differential equation of motion and the corresponding classical and non-classical boundary conditions are determined using the variational method. As an example, the free-vibration response of hinged-hinged microbeams is derived analytically using the Method of Multiple Scales. Also, the nonlinear size-dependent static bending of hinged-hinged beams is evaluated numerically. The results of the new model are compared with the results based on the linear strain gradient theory, linear and nonlinear modified couple stress theory, and also the linear and non-linear classical models, noting that the couple stress and the classical theories are indeed special cases of the strain gradient theory
  5. Keywords:
  6. Mid-plane stretching ; Non-classic continuum theory ; Classical model ; Classical theory ; Continuum theory ; Couple stress ; Couple stress theory ; Euler Bernoulli beams ; Free vibration ; Linear strains ; Method of multiple scale ; Micro beams ; New model ; Non-Linearity ; Nonlinear behavior ; Nonlinear partial differential equations ; Nonlinear strain ; Size effects ; Static bending ; Strain gradient theory ; Variational methods ; Boundary conditions ; Continuum mechanics ; Equations of motion ; Partial differential equations ; Vibration analysis ; Nonlinear equations
  7. Source: International Journal of Engineering Science ; Volume 49, Issue 11 , 2011 , Pages 1256-1267 ; 00207225 (ISSN)
  8. URL: http://www.sciencedirect.com/science/article/pii/S0020722511000176