Almost-Analytical Solution of Pucher’s Equation in Polar Coordinates

In architectural structural design, particular attention is given to shell structures that can carry their own weight under gravity through in-plane stresses alone, without bending action. These are known as membrane shells. Their shapes are obtained by solving an equilibrium equation called the Pucher’s equation. In this paper, we show that Pucher’s equation can be solved almost analytically. We then verify the resulting forms with finite element analysis (FEA) and demonstrate that the stress distributions computed in the FEA closely match those predicted in the form finding stage.