The thesis is structured with an initial introduction about the form finding and some motivation on the use and the necessity of this method in the engineering and architecture world. The thesis is based on Isogeometric Analysis, so a brief description of this technique is given in Chapter 1. In Chapter 2 the mathematical and mechanical ground for the element development is given. The concepts of point description, displacement and strain are described according to their use during the development. Beginning with the general description of the governing equations, the membrane and the cable are described according their assumption and features. Starting from the point description in the three dimensional space, all the necessary components for the derivation of the Principal Virtual Work are defined. This is the starting point for the element formulation described in Chapter 3. The discretization of position and displacement done with the NURBS shape functions, and all the relative derivatives, lead to the formulation of the external forces Fext, the internal forces Fint and the stiffness matrix Kint. The form finding process is described in detailed in Chapter 4. A description of the State of the Art of form finding, shows which elements are used nowadays, while a focus is done on the possible problems coming from a general description of this method. Starting from these limitations, the (Force Density Method FD) is analyzed and the URS (used to do the form finding in this thesis) is described referring to the initial work [BR99]. The elements and their use in form finding are tested according to academical benchmarks available in the literature. Chapter 5 collects the result of the test and shows the correctness of the presented implementation. Finally a summary and the conclusions of this thesis work are given in Chapter 6, with several proposal for possible further works.     «

The thesis is structured with an initial introduction about the form finding and some motivation on the use and the necessity of this method in the engineering and architecture world. The thesis is based on Isogeometric Analysis, so a brief description of this technique is given in Chapter 1. In Chapter 2 the mathematical and mechanical ground for the element development is given. The concepts of point description, displacement and strain are described according to their use during the developme...     »