The best known isotropic membrane stress state is a soap film. However, if we allow the value of the isotropic stress to vary from point to point then the surface can carry gravity loads, either as a hanging form in tension, or as a masonry shell in compression. The paper describes the theory of isotropic membrane stress under gravity load and introduces a particle method for its numerical simulation for the form finding of shell structures.
Aish, F., Joyce, S., Malek, S., & Williams, C. J. K. (2015). The use of a particle method for the modelling of isotropic membrane stress for the form finding of shell structures. Computer-Aided Design, 61, 24-31. https://doi.org/10.1016/j.cad.2014.01.014