Elastic gridshells comprise an initially planar quadrilateral network of elastic rods that is actuated into a three-dimensional shell-like structure by loading its extremities. This shaping results from elastic buckling and the subsequent geometrically nonlinear deformation of the grid structure. The first examples of architectural elastic gridshells appeared in the 1970’s but, to date, a limited number of these structures have been constructed around the world, primarily due to the challenges involved in their structural design. Yet, elastic gridshells are extremely efficient structures: they can cover wide spans with low self-weight, they allow for a variety of aesthetically pleasing shapes and their construction is typically simple and rapid. Developing predictive frameworks with mechanics at their core, which combine computational tools together with physically-based design guidelines, are important for the early stages of architectural design of this class of structures.
We study the mechanics of elastic gridshells by combining precision model experiments that explore the scale invariance of the problem, together with quantitatively predictive computer simulations that employ the Discrete Elastic Rods (DER) method. Our experimental samples are custom fabricated by first laying out a square grid (with a prescribed boundary contour) of Nitinol rods over an acrylic mold etched by a laser-cutter. An elastomeric polymer is then poured over the crossing nodes to cast joints with well defined mechanical and geometric properties. These joints impose positional constraints, but have negligible in-plane shearing stiffness and no bending-twisting coupling, thereby greatly simplifying the analysis. Each gridshell is then loaded by displacing the extremities of each rod along radial paths towards the center of the structure. The buckled configurations that ensue are digitized using a 3D laser scanner and their mechanical response is also measured.
In parallel, we perform computer simulations that employ the DER, a method that was originally developed by the computer graphics community for the simulation of hair. However, we have since shown that DER has remarkable predictive power for engineering mechanics problems involving large deformations of filamentary structures. In our computed elastic gridshells, the rods are connected to each other at the joints via springs, and the loading is applied by prescribing the displacement at their extremities. Excellent agreement is found between the experiments and simulations. Upon validation, the numerics are then used to broadly explore parameter space towards identifying general design principles for specific target final shapes. Our findings are rationalized using the theory of discrete Chebyshev nets, together with the group theory for crystals. Higher buckling modes occur for some configurations due to geometric incompatibility at the boundary and result in symmetry breaking. Along with the systematic classification of the various possible modes of deformation, we provide a reduced model for form-finding in elastic gridshells.