Eigenfunctions of crack problems in the Mindlin plate theory

Based on the Mindlin plate theory the eigenfunctions for a through‐thickness crack in a bending and twisting plate have been derived. The results are given as power series in terms of deflection, rotation and stresses. By introducing two auxiliary functions in the Mindlin plate theory we obtained two decoupled partial differential equations of the fourth and second order. This system of partial differential equations allows for each crack face to describe all three types of static boundary conditions. The first eigenfunction of the stress state shows the same singular near‐tip field at the crack tip known from two‐ and three‐dimensional crack analyses as well as from Reissner's plate theory. The second eigenfunction similarly characterizes the constant stress parallel to the crack as the T‐stress in plane elastic problems. Based on the Mindlin plate theory the eigenfunctions for a through‐thickness crack in a bending and twisting plate have been derived. The results are given as power series in terms of deflection, rotation and stresses. By introducing two auxiliary functions in the Mindlin plate theory the authors obtained two decoupled partial differential equations of the fourth and second order.