On the use of singular displacement finite elements for cracked plate in bending

Abstract

The objective of this work is to assess the performance, convergence and accuracy of four different displacement crack-tip elements used in modelling a cracked plate subjected to out-of-plane bending. A methodology is developed for calculating the singular field from the computed results and optimizing the mesh used in the numerical solution. It was found that using the quarter-node triangular elements surrounded by quadrilateral transition elements yields very accurate estimates of the singular fields of displacements and stresses as well as the stress-intensity factor for various materials and thicknesses of plates. It was also found that when the transition elements are incorporated, the optimum length of the singular element ranges from 0.5 to 1 per cent of half of the crack length.

On the strain energy release rate for a cracked plate subjected to out-of-plane bending moment

“…To represent the actual physical conditions, a refined model which allows contact on the compressive side is needed. Another important matter is that the nondimensionalized parameter e used in (10), (14) and (15) is taken infinitesimally small but not zero. It is not to be confused with a zero value which reduces the governing equations of Reissner plate theory to classical plate equations.…”

“…Wilson and Thompson [11] and Ahmad and Loo [12] used the classical plate element and extrapolated the near tip displacement to obtain the stress intensity factor. Singular element or special element considering transverse shear deformation was investigated by Yagawa and Nishioka [13], Wahba [14], and Viswanath et al [15]. The modified crack closure method was investigated by Viswanath et al [16] using CSA/NASTRAN.…”

Cracked plates subjected to out-of-plane tearing loads

“…Some researchers used classical plate theory [1][2][3][4][5][6][7][8], and some employed Reissner/Mindlin plate theory [9][10][11][12][13][14][15][16][17][18][19][20][21] for investigation. One peculiar result from these studies is that the stress intensity factors and near-tip stress distributions associated with classical plate theory are different from Reissner's plate solutions and that Reissner/Mindlin plate solutions do not approach classical plate solutions even as the ratio of plate thickness to crack size (h/a) approaches zero.…”

Influence of crack closure on the stress intensity factor in bending plates ? A classical plate solution

“…Some researchers used the classical plate theory [1][2][3][4][5] while some used Reissner's thick plate theory [6][7][8][9][10][11][12][13][14][15][16]. In both cases the crack face was modeled as a free surface in either the Kirchhoff or Reissner sense, and the compressive sides of crack surfaces were allowed to penetrate or overlap each other.…”

“…He ascribed the difference to the simplified boundary condition on the crack surface inherent in classical plate theory. No stress intensity factors were given by either Jones and Swedlow [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] or Heming [18]. Alwar and Nambissan 1-19] used a 3-D finite element method to model closure behavior at the crack face.…”