Dynamic plane deformation of semi-infinite polygonal plate: Kostrov's “paradox” and its amendment

Under dynamic loading of a concave isotropic wedge the usual formulas which express the displacement field through two potentials and applies for any convex wedge, lead to a strong singularity at the vertex and need to be improved (so-called Kostrov's correction). For an unbounded isotropic and homogeneous plane polygonal body, we derive a construction of the potentials providing true singularities of the displacement field in vertices of several “entering” corners. We also correct inaccuracies found in previous publications.