A novel shape optimization approach for strained gridshells: Design and construction of a simply supported gridshell

Abstract

Strained gridshells are reticulated shell structures that are erected from a flat grid of initially straight laths. The structural efficiency of a gridshell is determined by its shape, which is traditionally designed using form-finding techniques. However, these techniques are primarily used to generate structures in pure tension or compression for a single load case only. In cases where classic form-finding techniques are not applicable, such as for cantilevering gridshells or simply supported gridshells, numerical optimization can be used to find a suitable shape. In this paper, an optimization procedure is proposed that optimizes the shape of a strained gridshell for a given grid. The forces applied to erect the gridshell are chosen as the design variables. These erection forces are optimized to minimize the so-called end-compliance, which is defined as the inner product of the external loads and the resulting displacements. The method of moving asymptotes is adopted to solve the optimization problem and implicit dynamic relaxation is used to solve the nonlinear equilibrium equations. Geometric nonlinearity is taken into account by using co-rotational beam elements to model the gridshell laths. To validate the proposed approach, a 6×6 m2 prototype was built. The results show that this approach allows the structure to be optimized considering multiple load cases, while accounting for practical building constraints, and potential designer constraints.