Form-finding of elastic gridshell based on spatial elastica model

Abstract

In engineering design, elastic gridshells, which are composed of a number of elastic rods, are advantageous because they are lightweight, easy to construct, and low-cost as well as have a long-span space. However, the form-finding of a gridshell is challenging owing to the large deformation and strong geometric-nonlinearity of the structure.In this paper, a new form-finding method based on spatial elastica model (FMSE) is proposed. The deformations of elastic rods, obtained via the elliptic integral solution of spatial elastica, is integrated into the overall deformation of the gridshell. A set of transcendental equations is solved using the quasi-Newton method to ensure that the deformation of the gridshell satisfies the given boundary conditions. To validate the proposed FMSE method, desktop experiments (designed using the theory of Chebyshev nets) are performed on gridshells made of glass fiber reinforced polymer rods. The predictions of the FMSE method agree well with the experimental results.Accordingly, the proposed FMSE method is expected to have potential applications in elastic gridshells, on the investigations of form-finding, load-bearing capability, non-local deformation behavior, and also stability of structures.