Finite element analysis of cracked beams innovative weak form equations

A governing differential equation for the free vibration of cracked beam is derived in this paper. The closed form solution is obtained using this equation and is used to verify the governing equation. The finite element formulation commences with the weak form equation. In order to derive the weak form equation, the conventional method of weighted residual is used. The correct weak form equation is derived based on the physics of the proposed innovative model. In order to verify the accuracy, efficiency and robustness of the proposed method, a beam with classical boundary condition is analysed. It is shown that when the derivatives of the Dirac delta distribution appears in a differential equation the corresponding weak form equation cannot be obtained by the conventional method of weighted residual. The free vibration of cracked bars, stability and dynamic stability of cracked beams are all equally applicable by the proposed method.


  • English

Media Info

  • Media Type: Print
  • Features: Figures; References; Tables;
  • Pagination: pp 39-46
  • Serial:

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Filing Info

  • Accession Number: 01497395
  • Record Type: Publication
  • Files: TRIS
  • Created Date: Nov 1 2013 8:55AM