FURTHER CONSIDERATIONS OF STRESS-CONCENTRATION PROBLEMS FOR TWISTED OR SHEARED SHALLOW SPHERICAL-SHELLS

We extend earlier studies of closed-form and asymptotic solutions of t he problems of transverse twisting and membrane shearing of shallow sp herical shells with small circular traction-free holes or rigid insert s. Our first extension concerns a modified form of the relevant exact solution of the shell equations, so as to take advantage of the static -geometric duality property of linear shell theory. As a consequence w e observe that the results for two of the four previously considered p roblems can be seen as the static-geometric duals of the other two. Th e second extension concerns the formulation of a general boundary valu e problem, with the problems of the hole and the rigid insert as speci al cases. Furthermore, on the basis of this formulation we find, as a particularly simple boundary value problem of physical interest, the p roblem of a hole the edge of which is transversely fixed. The asymptot ic properties of the twisting and shearing solutions for this case are shown to be intermediate, in a specific sense, to the previously esta blished order of magnitude properties for the free hole or rigid inser t cases.