The boundary integral equation method applied to shallow membrane shells of positive Gaussian curvature

Abstract

The boundary integral equation method (BIEM) is developed for the analysis of shallow membrane shells with positive Gaussian curvatures. Shells with constant thickness and constant curvatures are considered. In the infinite domain, fundamental solutions are obtained which correspond to generalized concentrated tangential forces in the x and y coordinate directions. The Betti-Maxwell reciprocal theorem and Green's second identity are used to obtain the boundary integral equations of the solution presented. This approach, which is applied for the first time in membrane shell theory, seems to be a powerful alternative to domain type methods. Shells with various boundary conditions, loadings and arbitrary plan forms can be considered. It is also possible to add the effects of thermal fields and openings in the shells. The potential of the method is demonstrated by means of a worked example.