Computational methods for form finding and optimization of shells and membranes

Free form shells optimized for stiffness under given loading and membrane structures act in a pure membrane state of stresses, either because bending is minimized or not even present by definition. Physical experiments as soap films and hanging models have been used since centuries to generate optimal shapes of membranes in tension and shells in compression. The paper presents numerical methods to simulate the physical experiments as well as how they can be merged among each other and with the most general technology of structural optimization. The combined approach represents the combined power of each technique. Several examples illustrate the methods and typical applications.