Analysis of Noncircular Cylindrical Shells

A method is developed for the analysis of noncircular cylindrical shells by simulating the Donnell-Jenkins equation on a hybrid computer. The shell is assumed to be simply supported at ends but subject to any set of boundary conditions along the edges. For a uniformly loaded shell, the governing partial differential equations are reduced to ordinary differential equations using separation of variables. These equations contain variable coefficients that are functions of slope and curvature of shell arc. The slope is first expressed as a polynomial in terms of arc length and this polynomial and the curvature then are generated on the analog computer. It was found that once the basic simulation is set up, the model can be changed rapidly to include different cross-sectional profiles. Various methods of satisfying the split-boundary conditions on the hybrid computer are described and it is shown that the semiautomatic method employed by the writers leads to rapid convergence in the present case.