Tarcza Kołowa pod Wpływem Działania Siły Skupionej i Obciążenia Ciągłego // Pierścień Kołowy pod Wpływem Działania Danego Obciążenia
This paper contains first the derivation of equations determining the stresses Rθ, R, and θθ at any point of a circular disc with two continuously distributed loads q and p acting on the periphery and then - the derivation of the analogous equations for a concentrated load Q and a continuously distributed load p.
A solution of the problem of an isotropic circular ring subjected to an arbitrary load on the inner and the outer circle. This problem reduces essentially to the determination of two unknown analytic functions, φ(z) and F(z), appearing in the equations for the stresses Rθ, R, and θθ (Fig. 1), and the corresponding displacements Ur, uo for any point of the region. Using the relations between the value of an analytic function at any point of a ring region, and its real and imaginary part on the inner and the outer circle, final equations (24) and (25) are derived for the functions θ(2) and F(z).
H. Villat, Le problème de Dirichlet dans une aire annulaire, Rendiconti del Circolo Mathem. di Palermo, t. 33, 1912.