Investigating principal lines and R-Funicularity patterns on shells

The relationship between form and structure has become a renewed area of interest; one reason for this is the increasing need to encourage energy savings from a sustainability standpoint, which requires optimizing material utilization. Curved spatial structures can exemplify geometric optimization when they are conceived as shape-resistant systems. By following the predominant force-flow paths, such structures can make lightweight architecture and efficient material use achievable. Shell structures are a highly relevant topic, with their various manifestations in continuous and lattice shells, and in a wide range of materials, from reinforced concrete to wood. There are numerous examples of the use of this form in contemporary architecture, as well as in scientific research. This research aims to promote the integration of structural concepts at the early stages of design by developing a methodological tool for structural analysis and conception of form. The creation of this tool is primarily based on the study and visualization of streamlines, achieved through the implementation of a script in the Grasshopper environment. Streamlines are a family of curves traced on a surface that have the property of being tangent at every point to an assigned vector field. Since both the geometric properties (such as curvature) and mechanical properties (such as principal normal forces and bending moments) of a structure constitute vector fields, these lines can be used to represent their behavior. Streamlines are an effective tool for visualizing mechanical analysis results, as they illustrate the natural flow of forces within the structural system, suggesting ideal reinforcement layouts and ensuring material continuity. In literature, research on streamlines has focused primarily on generating principal stress lines for the purpose of using them in the topological definition of gridshell systems. This thesis introduces a new family of streamlines: eccentricity lines, based on the principle of R-funicularity. These lines are particularly interesting from a mechanical standpoint, as they provide a synthesis of membrane stress states and bending moments. To validate the proposed method, the thesis will present the analysis of significant examples of shell structures, exploring the potential use of streamlines in shape generation. The ability to generate multiple families of lines within the same environment where the shape is designed (Grasshopper3D) enhances the possibilities for exploration and understanding. This research underscores the importance of integrating computational tools, including graphical ones, into structural design, promoting a design approach that affirms the need for the coexistence of structural and architectural principles. To translate the research outcomes into a practical resource for designers, a custom Grasshopper plug-in named RFun has been developed and is documented in Appendix A. Written in CPython on the RhinoCommon API, RFun automates the evaluation of generalized eccentricity, plots RF-ellipses, and generates streamline families—including the new eccentricity lines—directly within the parametric modelling environment. The plug-in is intended as an accessible, open tool that allows architects and engineers to experiment with Relaxed Funicularity concepts during early-stage form exploration.