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Large-scale spatial skeletal structures belong to a special kind of 3D structures widely used in exhibition centers, supermarkets, sport stadiums, airports, etc., to cover large surfaces without intermediate columns. Space structures are often categorized as grids, domes and barrel vaults. Double layer grid structures are classical instances of prefabricated space structures and also the most popular forms which are frequently used nowadays.Topology optimization of large-scale skeletal structures has been recognized as one of the most challenging tasks in structural design. In topology optimization of these structures with discrete cross-sectional areas, the performance of meta-heuristic optimization algorithms can be increased if they are combined with continuous-based topology optimization methods. In this article, a hybrid methodology combining evolutionary structural optimization (ESO) and harmony search algorithm (HSA) methods is proposed for topologyoptimization of double layer grid structures subject to vertical load. In the present methodology, which is called ESO-HSA method, the size optimization of double layer grid structures is first performed by the ESO. Then, the outcomes of the ESO are used to improve the HSA. In fact, a sensitivity analysis is carried out using an optimization method (ESO) to determine more important members based on the cross-sectional areas of members. Then, the obtained optimum cross-sectional areas of members are used to enhance the HSA through two modifications. Structural weight is minimized against constraints on the displacements of nodes, internal stresses and element slenderness ratio. In topology optimization of double layer grid structures, the geometry of the structure, support locations and coordinates of nodes are fixed and this structure is assumed as a ground structure. Presence/absence of bottom nodes, and element cross-sectional areas are selected as design variables. In topology optimization of the ground structure, tabulating of nodes is carried out based on structural symmetry: this leads to reduce complexity of design space and nodes are removed in groups of 8, 4 or 1. The presence or absence of each node group is determined by a variable (topology variable) which takes the value of 1 and 0 for the two cases, respectively. The ground structure is assumed to be supported at the perimeter nodes of the bottom grid. Therefore, these supported nodes will not be removed from the ground structure. In order to achieve a practical structure, the existence of nodes in the top grid will not be considered as a variable. This causes the load bearing areas of top layer nodes to remain constant. Also, discrete variables are used to optimize the cross-sectional area of structural members. These variables are selected from pipe sections with specified thickness and outer diameter. Therefore, in topology optimization problem, the number of design variables is the summation of the number of compressive and tensile element types and the number of topology variables. The proposed approach is successfully tested in topology optimization problem of double layer grid structure. In particular, ESO-HSA is very competitive with other metaheuristic methods recently published in literature and can always find the best design overall. Also, it is determined that HSA method can find better answer in the topology optimization of large-scale skeletal structures, in comparison to optimum structures attained by the GSA and ICA.

Keywords: Skeletal structures, Double layer grid structures, Topology optimization, Evolutionary structural optimization, harmony search algorithm.

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