Inner boundary conditions of mindlin plate with a finite-length part-through crack

In this paper, the inner boundary conditions of a simply supported rectangular Mindlin plate with a finite-length Part through crack is first obtained. The part-through crack on the plate surface having an arbitrary length and depth is assumed to be open, non-propagating and parallel to one side of the plate. Based on Mindlin plate theory and Hamilton theory, we got the governing equations of motion. Then, the rectangular plate is decomposed into two domains and an artificial spring with a varying stiffness along the crack is used to describe the elastic behavior of the plate at the interconnection boundaries between two domains. We got the strain energy release rate (G) through the stress intensity factor (K). Then, the rotary discontinuity condition is acquired. After complex derivation, we obtained the inner boundary conditions of rectangular cracked Mindlin Plate.