AbstractThe problem of stress determination in the area of cut‐outs in circular cylindrical shells at given loads is of great interest in industrial practice. This work deals with a mixed boundary value problem of a differential equation derived according to the theory of shallow shells. On partCt1of the boundary, the displacements are given, whereas the stresses are specified on the remaining partCt2. Starting from the Betti‐Maxwell principle and with the aid of the fundamental solutions for unit loads and unit displacements, integral representations can be derived for the displacement functions as well as the stress functions.The problem is then transformed into an equivalent system of Fredholm integral equations of the first kind with logarithmic kernels as the main part. As the integral equations together with the auxiliary conditions form a strongly elliptical system of pseudo‐differential operators, the Galerkin method converges. Assuming that curvesCt1andCt1do not have points of intersection and that the data are sufficiently regular, the required functions are approximated by cubic splines and, for simplicity's sake, the integral equation system is solved by approximation with a collocation method. In view of the complicated terms of the kernel functions, the kernels are split into a regular and a singular part, the regular part being in turn replaced by cubic splines. The remaining integrations are done numerically by means of Gaussian quadrature formulae. The applicability of the method is demonstrated with the example of a cylinder under internal pre
展开▼
