Keywords: optimum structural design, harmony search algorithm, minimum weight, stochastic search technique, lamella domes.

Domes provide flexibility and economy to engineers and architects for covering large areas such as exhibition halls, stadiums, concert halls, shopping centres and swimming pools. Domes supply unimpeded wide spaces and they encompass a maximum amount of areas with a minimum surface. They are also exceptionally suitable structures for covering places where minimum interference from internal supports are required. These specifications of domes make them very economical structures when they are compared with the classical structural types in terms of consumption of construction materials. Domes are structural systems which include one or more layers of elements that are arched in all directions. The surface of a dome may be a part of a single surface such as a sphere or parabolic, or it may consist of a patchwork of different surfaces. Further, domes are either formed by using curved members forming a surface of revolution or by straight members meeting at joints which lie on the surface.

Today a great majority of domes are constructed as steel braced domes. These spectacular latticed domes are made out of tubular members and preferred due to their lightness and elegance. There are several types of latticed domes such as Schwedler dome, geodesic dome, lamella dome and network domes. Large numbers of latticed domes that are built recently are lamella type. They comprise a great number of interconnecting steel elements, called lamellas. The stresses are distributed evenly in these domes. They can easily take a large concentrated or live load that are rapidly dispersed throughout the framework; generating primarily axial forces in lamella units. This results in substantial saving of material. Due to their great structural rigidity and low cost, the lamella dome has been selected for the world's biggest steel dome that covers 300m span.

In this study optimum topology design problem of lamella domes is considered. The total number of rings, the height of the crown and the sectional designations for the groups of members of a lamella dome are taken as design variables. The steel pipe sections of the LRFD-AISC (Load and Resistance Factor Design- American Institute of Steel Constitution) are adapted for the members of the dome. The design constraints are implemented from LRFD-AISC. In the prediction of the response of the dome under the external loads the geometric nonlinearity is considered. The overall stability check is carried out during the nonlinear analysis iterations to ensure that the structure does not lose its load carrying capacity due to instability. The formulation of such a design problem turns out to be a discrete programming problem. The harmony search algorithm is used to determine the solution of the design problem. This algorithm is a recent addition to the stochastic search techniques of combinatorial optimization problems. The design example considered demonstrates the robustness of the algorithm presented.

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