Integral-equation solution for half planes bonded together or in contact and containing internal cracks or holes

Research paper by G. Tsamasphyros, P. S. Theocaris

Indexed on: 01 Jul '83Published on: 01 Jul '83Published in: Archive of Applied Mechanics


The complex potentials Φ(z) and Ψ(z) describing the stress-field due to a concentrated force, or a dislocation, applied at some point at the interior of either of the half planes bonded together, or being under some kind of contact between them, are calculated. By using these potentials as Green's functions we have reduced the problem of crack and/or holes existing in either of these half-planes to an integral equation along the cracks or holes. The advantage of the method is that the integral equation along the interface between the two half-planes (y=0) is canceled out. Thus, the numerical evaluation of the state of stress is considerably reduced and simplified. The respective integral equations corresponding to some characteristic cases of bimaterial plates were derived. Finally, examples of cracked half-planes, either stressor displacement-free, or bonded with other half-planes, indicated the potentialities of the method.