Direct Minimization Approaches on Static Problems of Membranes

Within this work, direct minimization approaches on static problems of membranes are discussed. In the first half, standard direct minimization methods are discussed. Some form-finding analyses of tension structures are also illustrated as simple direct minimization approaches. In the second half, the principle of virtual works for cables, membranes, and 3-dimensional bodies are examined and they are approximated in a common way by using Galerkin method. Finally, some examples that direct minimization approaches can solve are reported.