Mathematical Problems in Engineering
Volume 2005 (2005), Issue 3, Pages 377-389

Conditions of cracking of a stringer

D. I. Bardzokas and G. I. Sfyris

Laboratory of Strength and Materials, Department of Mechanics, Faculty of Applied Mathematics and Physics Sciences, National Technical University of Athens, Zographou Campus, Theocaris Buildings, Athens 15773, Greece

Received 13 December 2002

Copyright © 2005 D. I. Bardzokas and G. I. Sfyris. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the limits of brittle failure of materials, we investigate the problem of possible cracking of an infinite stringer on the boundary of an elastic half-infinite plate. The plate is exposed to tensioning by uniformly distributed forces, and also to contact stresses due to application of forces on the stringer. The accurate solution of a contact problem of interaction of an infinitely continuous stringer is constructed. With the help of this solution, we formulate the condition of cracking of a stringer and the necessary restrictions for external loading, which provide the contacts of a broken stringer with a plate without propagation of a crack inside the stringer. The problem considered here is of interest for theory and practice. We firstly formulate the modified problem of E. Melan and with the help of Fourier integral transformation, we construct its acoustic solution and then formulate the condition of cracking of an infinite stringer. After that, reveal the necessary restrictions on external loadings, which provide the contact of the failed stringer with a plate without propagation of the crack inside the plate.