Mixed Isogeometric Form Finding Of Lightweight Structures

Cables and membranes structures are among the most used lightweight structures for large span applications. They are widely known as optimal systems since they adapt their shape which is not known a priori to the flow of forces transmitting applied loads to the supports by pure tension forces. The form finding process plays a crucial role for these non conventional structures. Thus starting from a detailed analysis of the state of the art, in the present work the attention has been given on the Force Density Method and the Updated Reference Strategy applied to cables and membranes. These methods have been examined by means of numerous applications highlighting their main limit that is the lack of a robust variational setting and consequently a not precise defined stopping criterion for the solution process. For these reasons starting from a 2 fields (for cables) and 3 fields (for membranes) re-formulation of the Hu-Washizu principle, a new mixed form finding strategy has been introduced in this thesis. Two classes of problems have been analyzed: one with kinematics constraints (the catenary with fixed length) and another with constraints on the stress state (the problem of minimal surfaces). The mixed variational form finding has been implemented using isogeometric interpolation. Thus the isogeometric analysis has played a key role within the work because it allowed the interoperability between CAD and structural analysis avoiding the model conversion to a polygonal mesh and integrating the accuracy of freeform CAD geometries within the structural model. In the present work Rhinoceros3D and its visual scripting Grasshopper3D environment have been used as preprocessor and postprocessor to create and visualize the resulting geometry. Comparisons of the results obtained through the mixed isogeometric form finding with those of the updated Force Density Method and the Updated Reference Strategy underline the advantages of the proposed formulation particularly consisting in smooth and reliable stress distributions needing a very limited number of iterations.