Proceedings of the 1. Conference on Applied Mathematics and Computation Dubrovnik, Croatia, September 13–18, 1999 pp. 223–232 Some Numerical Models of Fabric Structures Kreˇ simir Fresl ∗ Abstract. Form finding as the first phase of design of fabric structures is considered, with a minimal surface as a plausible mathematical model. Analysis is restricted to structures with fixed edges. A comparison is made of the two discretizations of the differential equation of minimal surface and the pertaining functional, namely, the finite difference and the finite element discretizations. Resulting system of nonlinear algebraic equations is solved by a variant of the full multilevel method with full approximation storage scheme. Numerical studies confirm that the multilevel method can be used as a robust and a stable solver with a fast convergence for both types of discretizations. AMS subject classification: 74–04, 74G65, 74K15, 49Q05, 65N55 Key words: fabric structure, form finding, minimal surface, multigrid method 1. Introduction: on tensile fabric structures Tentatively, we can define fabric structures as building structures that are pri- marily used for enclosure of large spaces, particularly those with wide spans clear between supports, and whose basic building material is (structural) fabric, acting as a membrane. Fabric is thus used both as a load bearing structure and as an enclosure [1]. Conventional massive and rigid structures can, by means of internal distribu- tion of stresses, resist different kinds of stresses: tension, compression, shear. Stress distributions lead to complex stress patterns that can be observed in photoelastic ex- periments. Flexible ropes and fabric, on the other hand, can transmit only tension. They are, however, very efficient since they carry applied load by direct route, along their center line or middle surface, while the distribution of tensile stress is uniform (and they cannot “avoid” carrying load by buckling, as compressive members do). Single rope or flimsy membrane will noticeably alter its shape when load changes its position or direction. Other means are therefore needed to give stability and stiff- ness to a structural system which is made up of flexible components or material. Cables must be arranged in a net; in a simple case there are two orthogonal families of cables: load bearing, concave cables in one direction, and stabilizing, convex cables in another. Similarly, fabric membrane must form an anticlastic surface. At the same time, cables and fabric must be subjected to a particular pattern of prestress, since tension should * Faculty of Civil Engineering, University of Zagreb, Kaˇ ci´ ceva 26, 10000 Zagreb, Croatia, e–mail: fresl@grad.hr