The study of debonding is of importance in providing a good understanding of the bonded interfaces of dissimilar
materials. The problem of debonding of an arbitrarily shaped rigid inclusion in an infinite plate with a point dislocation
of thin plate bending is investigated in this paper. Herein, the point dislocation is defined with respect to the difference
of the plate deflection angle. An analytical solution is obtained by using the complex stress function approach and the
rational mapping function technique. In the derivation, the fundamental solutions of the stress boundary value problem
are taken as the principal parts of the corresponding stress functions, and through analytical continuation, the problem
of obtaining the complementary stress function is reduced to a Riemann-Hilbert problem. Without loss of generality,
numerical results are calculated for a square rigid inclusion with a debonding. It is noted that the stress components are
singular at the dislocation point, and a stress concentration can be found in the vicinity of the inclusion corner. We also
obtain the stress intensity of a debonding in terms of the stress functions. It can be found that when a debonding starts
from a corner of the inclusion and extends to another corner progressively, the stress intensity of the debonding increases
monotonously; once the debonding extends over the corner points, the value of the stress intensity of the debonding
gradually decreases. The relationships between the stress intensity of the debonding and the direction and position of the
dislocation are also presented in this paper.
Form-Finding of Shells Containing Both Tension and Compression Using the Airy Stress Function