Fractal geometries, inspired by patterns found in nature, offer a powerful framework for generating complex and adaptive forms through simple recursive rules. The application of these geometries in architectural design may enhance the structural efficiency. In this regard, this paper aims to evaluate the behavior of fractal grid-shell structures under both symmetric and asymmetric loading conditions. In order to assess the influence of different generation methods on the structural performance, the assumed fractal pattern is created based on three different strategies, including (a) a fully stochastic approach, (b) a deterministic approach with constant ratios in all iterations, and (c) a deterministic approach with independent ratios in each iteration. A conventional grid-shell structure with square cells is also adopted for comparison purposes. The generated planar patterns are mapped to three surfaces with different characteristics (i.e., spherical, hyperboloid, and hyperbolic surfaces) to form grid-shell structures. To achieve the optimal design of the considered structures, both single and multi-objective optimization approaches are used. Structural mass and maximum deflection are considered as two main goals to be minimized. The results highlight the effectiveness of fractal grids, in particular those created through the third strategy, in achieving optimized, lightweight structural systems under both loading conditions. The finding is confirmed through the comparison of structural mass in constant deflections and evaluating their stress and deflection distribution contours.
Shahbazi et al. (Tue,) studied this question.