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Fig. 2. Decomposition of the coupled membrane-plate problem by means of superposition, here shown for in-plane loading.
notch edge results,
III: an inï¬nite notched plate with the corresponding loads at the notch edge.
Looking at this decomposition from a diï¬erent point of view, the solution for
the stress concentration problem of a notched plate with a loaded cut-out
is derived by superpositioning of the solutions for the problem of a notched
plate with an unloaded hole and a loaded outer boundary (subproblem I and
II) and the problem of an notched plate with a loaded cut-out and an unloaded
outer boundary (subproblem III). Of course, if dealing with the problem of an
unloaded cut-out, subproblem III can be omitted.
Subproblem I, the ï¬nite plate loaded on the outer boundary by constant edge
forces and moments, can be solved elementarily and the solutions provide the
dynamic boundary conditions for subproblem II, i. e. the force and moment
resultants that have to be applied to the boundary of the notch in subproblem II so, that by superposition of I and II an overall unloaded notch edge
results. Since the method of complex-valued displacement functions is not applicable here, the Ritz-method is called upon for the solution of each of the
subproblems II and III, respectively. By superposing the solutions of all three
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