Dear Researchers,
I am using the classical Muskhelishvili method to solve plane stress problems in perforated plates with cracks. By introducing a conformal mapping function, the hole boundary is mapped onto the unit circle in the ζ-plane, then the boundary problem is solved on the unit circle. However, I have found that under certain mapping functions, the complex potential function has no solution (an ill-posed problem).
Is this an issue with the conformal mapping functions, or does this method inherently have this flaw?
In addition, when constructing the mapping function, I combined function of the square hole without cracks, denoted as omega1(zeta), with one of the unit circle hole with cracks, denoted as omega2(zeta), to create a composite function representing a square hole with cracks, denoted as omega = omega1(omega2(zeta)). Although I have checked that the graph of this composite function is correct, I have faced difficulties in solving complex potential functions for certain crack sizes. This has been troubling me for a long time.
I hope to receive your discussion or assistance regarding this issue.
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