Abstract
We consider a dome, modeled as a thin membrane of revolution, closed at the vertex and of unit height as shown in Figure 1. The membrane is loaded at the vertex by a force P, perpendicular to the axis of symmetry, and constrained at the base so that only membrane forces are transmitted to the ground. On assuming that the shape of the meridian is unknown, but the total volume, product of the surface area for the thickness, is given, we try to find the profile of the meridian which minimizes the highest stress at the base. It cannot yet be shown that the full problem admits a solution. However, comparison between some particular cases may give an idea of what the best shape of the dome must be.
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