Problem of a randomly oriented crack in a box-shaped shell

This paper deals with the stress state of a box-shaped shell formed by two semi-infinite plates joined at a right angle. The plates are homogeneous but have different thicknesses. The shell is weakened by a finite rectilinear crack of unit length which reaches one edge of the shell. The orientation of the crack and the load on its edges are arbitrarily chosen. The problem is solved with the assumption that the thickness of the plates is small compared to the length of the crack, which allows an asymptotic formulation of the problem. The problem is reduced to a special type of Riemannian vector problem in which the stress-intensity factor allows matrix factorization in accordance with Khrapkov’s scheme. The asymptotes of the resulting solution and the stress-intensity factor are examined in relation to the thickness of the shell and the angle formed by the crack and the edge of the shell. Translated from Prikladnaya Mekalinika, Vol. 34, No. 12, pp. 48–54, December, 1998.