A discrete topology optimisation method with feature size control for partial double-layer gridshell design

A density-based topology optimisation method for discrete structures with minimum and maximum feature size control of solid phase is proposed in this paper. The feature size of solid phase is defined as the radius of the minimal circumscribed circle of solid elements. The minimum feature size is achieved by density filtering and Heaviside projection while the maximum feature size is enforced by limiting the local material amount. Firstly, the proposed method is tested on a planar structure to demonstrate the successful control on minimum and maximum feature size of solid phase, as well as to reveal the effect of parameters. Then, the method is applied to a single-layer gridshell to identify the optimal material distribution under the uniformly distributed load. Based on the optimisation results of the single-layer gridshell, second-layer grids are added to form partial double-layer gridshells. Linear static analysis is carried out to investigate the mechanical properties of the obtained gridshells. Results show that, under the external load, the stress and displacement distributions within the whole structures are rather uniform, except for the support regions and the mid-span areas between the neighbouring supports.