Symmetric BEM for fracture mechanics of thin plates

A direct Symmetric Galerkin Boundary Element Method for the analysis of fractures in thin (Kirchhoff) infinite elastic plates in bending is presented as a particular case of a general formulation. Numerical difficulties due to the presence of highly singular integrals are overcome exploiting an analytical regularization procedure. Only weakly singular double integrals need to be computed. Two topics are addressed: evaluation of the stress intensity factors from the near-tip displacement and normal-slope fields and computation of the energy release rate by means of a sensitivity analysis procedure. In order to obtain a better accuracy special tip elements have been developed allowing to simulate the correct asymptotic behaviour of the variables involved. The procedure outlined can be applied to arbitrary crack shapes: numerical examples are provided for straight and circular fractures in infinite plates subject to bending moments and vertical shears. Comparisons between analytical and numerical results validate the ideas presented in this contribution.