Corner singularities in bi-material Mindlin plates

An eigenfunction expansion solution is first developed to find stress singualrities for bi-material wedges by directly solving the governing equations of the Mindlin plate theory in terms of displacement components. The singularity orders of moments and shear forces at corners are determined from the corresponding asymptotic solutions having the lowest order in r and satisfying the radial boundary conditions and continuity conditions. The present solution is applied to thoroughly examine the singularities occurring at the interface joint of bonded dissimilar isotropic plates and at the vertex of a bi-material wedge with two simply supported radial edges. The corresponding characteristic equations for determining the singularity orders of moments and shear forces are explicitly given. The singularity orders of moment are shown in graphic form as functions of the flexural rigidity ratio and corner angle, while the shear force singularity orders are given as functions of the corner angle and the shear modulus ratio multiplied by the thickness ratio. The order of moment singularity obtained here for bonded dissimilar plates is also compared with that based on the classical plate theory.