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of the function are of the same order. So the solution method of complex
valued displacement functions, as used for the solution of the generalized plate
equation in context of the classical laminate theory (for example in [10]), is
not applicable here.
In this study, an inï¬nite plate with a ï¬nite circular cut-out is selected as a
mathematical equivalent model for the notched plate and the following restrictions as for the loading conditions are introduced. The notched plate should
be loaded at the inï¬nite outer boundary by constant edge forces per unit
length Nx , Ny , Nxy (Fig. 1(a)) and constant edge moments per unit length
Mx , My , Mxy (Fig. 1(b)) in such a way, that the static equilibrium conditions
are fulï¬lled automatically when looking on the overall plate. At the edge of
the notch, the plate can be loaded by a constant normal edge force per unit
length Ni and a constant edge bending moment per unit length Mi (Fig. 1(c)).
(a) force resultants
(b) moment resultants
(c) force and moment resultant
Fig. 1. Boundary conditions on cut-out and outer boundary
In order to take into consideration the eï¬ect of the loads on the outer boundary
on the stress concentration problem of an inï¬nite plate, the actual state of
stress is decomposed using the superposition principle into three states of
stress (Fig. 2) as follows
I:
a ï¬nite, unnotched plate with loads at the outer edge,
II: an inï¬nite notched plate with loads at the edge of the notch, adapted
in such a way that, with superposition of I and II, an overall unloaded
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