A mixed boundary problem for a finite internally cracked plate

A displacements and resultant forces model (see eqns 2–5, 13 and 17) for a finite internally cracked plate is proposed. This model satisfies: (a) The equilibrium and compatibility condition in the region occupied by cracked plate; (b) Stress free condition on the surface of crack; (c) Single value condition of displacements around the crack. In this model, some undetermined coefficients are contained, these coefficients are derived from outer boundary condition.

It is proved that, this model is convenient not only for the displacements or resultant forces boundary problem, but also for the mixed boundary problem. Besides this, if the boundary problem is solved, to find the value of displacements of any points in cracked body is also convenient.

Two mixed boundary problems, one for the square cracked plate (see Fig. 3), and another for circular cracked plate (see Fig. 5), are solved. The numerical results obtained are shown in Tables 1 and 2 and Figs. 4 and 6 respectively. These results can explain how the constraint affects the values of the stress intensity factor on the crack tips.