Mechanical form-finding of timber fabric structures

How about fastening a knot? not with ropes... but with timber panels. Timber Fabric Structures (TFS) originate from such an inspiration. An architectural reinterpretation of fabric techniques (mainly braiding) using building scale timber panels to design lightweight timber spatial structures. TFS design raises challenges on both geometrical and structural facets: we would like to predict their relaxed deformed shape based on an arbitrary design pattern, but also the stress state introduced through the assembly, in order to be able to size panels and connections. The three-dimensional geometry of the TFS is behavior-based: it is the equilibrium state of its flexible structural components actively curved under the overlap order constraints. Panels bend, twist and buckle to meet the interlacing pattern and in braided configurations, contact might also occur between panels over the cross section and/or faces. Our form-finding tool is expected to meet three requirements: (i) come with an interpretation for interlacing as coupling constraints to be applied on flexible bodies which represent panels (ii) implement a flexible body kinematics which enhances twist degrees of freedom and (iii) take into account the panel intersection detection and handling. We cross two avenues toward structural form-finding of TFS. We first investigate the use of FEM techniques, suitable to handle the finite rotation regime and the complex contacts occurring while interlacing panels. We demonstrate the possibility, yet complexity, of reproducing the geometry of panel interlaced structures using a pseudo-dynamic framework with nonlinear shell Finite Elements. Such expensive bespoke simulation, yet precise, would limit the generative exploration of the TFS morphology, while besides it would be necessary to know the exact interlacing sequence in order to reproduce it. In search for the form-exploration freedom, in the second avenue we inspire from the physically-based modeling in Computer Graphics for our structural form-finding purpose. We are interested in the physics-based models to simulate flexible thin panels in order to propose an approximative but efficient simulation alternative to the FEM. The current physics-based frameworks used in the architectural form-finding are mostly particle-based modeling engines which can hardly manipulate twisted flexible objects, neither correctly reproduce out-of-plane bending behavior of the thin shell bodies. Two flexible body models derived from the discrete differential geometry, are inspected and employed in our study: a discrete Kirchhoff rod model based on the curve-angle kinematic with twist and bending degrees of freedom and a discrete elastic shell model for deformable triangular mesh surface manipulation with membrane and flexural energies. We exploit the rod model in a nonlinear static framework in order to virtually buckle, twist and interlace an initially flat set of panels of given length and span. The deformed configuration coming out of the static simulation is not however always intersection free, depending on design parameter inputs. The intersection resolving is performed in a dynamic framework with panels now simulated as thin plates and with the help of a surface intersection contour minimization algorithm for mesh surfaces. [...]