Stress concentration for a circular hole in a strip by singular integral equations
In recent work [e.g. the authors, Ing.-Arch. 57, 3-15 (1987; Zbl 0598.73102)] the plane elasticity problem of the infinite strip weakened by cracks and/or holes has been considered in general. In this work the method is applied to the problem of a strip weakened by a circular hole. A numerical solution is determined and the maximum stress concentration factor reported for a number of parameter values characterizing the circular hole in the strip. At first the basic principles of the method adopted are explained, and the unknown dislocation density function \(\omega\) (t) is introduced. Then a rather simple study is made and properties derived for the singular integral equation (S.I.E) and the solution (the complex potentials) in the non-physical region, the disc, is added. It is shown that the solution \(\omega\) (t) is defined up to a purely imaginary constant c associated with the solution within the disc (not affecting the solution in the physical region). A further condition is introduced to uniquely determine \(\omega\) (t) and the potentials within the disc. Furthermore using the derived properties of the S.I.E., it is shown that the S.I.E. can be modified in form to include this condition plus the condition of single-valuedness of displacements. Subsequently the modified S.I.E. is numerically solved for the problem and the stress concentration factor determined directly from \(\omega\) (t).
scientific article; zbMATH DE number 4016392