Two-sided contact of doubly connected symmetrical acute-angled stamps with curvilinear hole in infinite plate (Q2759515)

An infinite plate has regular polygonal hole with \(N\) rounded vertices. Two rigid symmetrical stamps with angular points are embedded into the hole and are equilibrated by two forces of equal magnitudes acting in opposite directions. The problem consists in determination of contact zones and contact stresses. First, conformal mapping of exterior of a unit circle onto the plate is performed by the formula \(Z=\omega(\xi)= R_0(\xi +\varepsilon/\xi^{N-1})\). The problem is reduced to a system of four singular integral equations with logarithmic kernels. In a general case solution of the system is difficult. Under the absence of friction sought functions has square-root singularities at the ends of contact zones and solution can be found by the collocation technique. Results of calculation for triangle hole are presented.