Tikhonov regularization for the modified mapping-collocation method applied to circumferential crack in a curved beam

AMIREGHBALI A., ÇÖKER D.

Joint 11th World Congress on Computational Mechanics, WCCM 2014, the 5th European Conference on Computational Mechanics, ECCM 2014 and the 6th European Conference on Computational Fluid Dynamics, ECFD 2014, Barcelona, İspanya, 20 - 25 Temmuz 2014, ss.1604-1611, (Tam Metin Bildiri) identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Basıldığı Şehir: Barcelona
  • Basıldığı Ülke: İspanya
  • Sayfa Sayıları: ss.1604-1611
  • Anahtar Kelimeler: Curved crack, Fracture mechanics, Modified mapping-collocation method, Stress intensity factor, Tikhonov regularization
  • Samsun Üniversitesi Adresli: Hayır

Özet

The modified mapping-collocation (MMC) method is applied to the problem of an isotropic curved beam with a circumferential crack under pure bending moment. Using least squares method to solve the overdetermined system of boundary condition equations causes numerical difficulties. Alternatively zeroth-order Tikhonov regularization is applied to solve the system. The regularization technique appears brilliantly helpful in eliminating the convergence problems associated with ill-posedness of the problem. The boundary condition satisfaction is examined. The results of stress analysis are in good agreement with that of the finite element method.