A plane stress linear elastic problem is proposed for two opposed point loads
applied at the center of a linear slot with rounded ends in an infinite plate. A
Kolosov–Mushelishvili solution technique is applied to this problem. A conformal
mapping function is found that transforms the slot geometry in the plane onto the
surface of a circular cylinder. As the mapping function contains branch points, a
series expansion of the coordinates is necessary in order to obtain an approximate
solution to the original problem. A simple expression for an equivalent slot is given
for an elliptical hole.
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