Singularity analysis of near-tip fields for notches formed from several anisotropic plates under bending

In this paper, we dealt with the problems concerning the singularities in the vicinity of a notch tip, or a crack tip as its special case, formed from several anisotropic plates subjected to bending and shearing forces. Attention was focused on the near-tip asymptotic analysis in monoclinic materials, which can be considered as the most general anisotropy in plate structures. The Reissner assumptions of the plate theory were adopted. First, the fundamental equations for a monoclinic plate were established in the cylindrical coordinate system by means of the Hellinger–Reissner variational principle. Second, by introducing the suitable dual variable vectors, the governing equations were established in the frame of the Hamiltonian system. These governing equations are particularly efficient to deal with multi-material problems because all variables used are continuous across the interfaces. Third, a simple but highly accurate numerical algorithm was proposed to resolve the governing equations. Finally, several numerical examples have been given in order to test the efficiency and the simplicity of the present theory in studying the asymptotic fields in the vicinity of a notch tip formed from several anisotropic plates