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A bending theory for beams with vertical edge crack

Ebrahimi, A ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. DOI: 10.1016/j.ijmecsci.2010.03.004
  3. Publisher: 2010
  4. Abstract:
  5. In this paper a linear continuous theory for bending analysis of beams with an edge crack perpendicular to the neutral plane subject to bending has been developed. The model assumes that the displacement field is a superposition of the classical EulerBernoulli beam's displacement and of a displacement due to the crack. It is assumed that in bending the additional displacement due to crack decreases exponentially with distance from the crack tip. The strain and stress fields have been calculated using this displacement field and the bending equation has been obtained using equilibrium equations. Using a fracture mechanics approach the exponential decay rate has been calculated. There is a good agreement between the analytical results from solving the differential equation of cracked beam and those obtained by finite element method
  6. Keywords:
  7. Bending ; Stress field ; Analytical results ; Bending analysis ; Bending equation ; Bending theory ; Cracked beams ; Displacement field ; Edge cracks ; Equilibrium equation ; Euler Bernoulli beams ; Exponential decay rates ; Fracture mechanics approach ; Load deflection ; Neutral plane ; Stress-strain ; Vertical crack ; Vertical edges ; Crack tips ; Decay (organic) ; Differential equations ; Fracture mechanics ; Finite element method
  8. Source: International Journal of Mechanical Sciences ; Volume 52, Issue 7 , July , 2010 , Pages 904-913 ; 00207403 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0020740310000470