Keywords: optimum design, space structures, genetic algorithm.

Space structures are some special three-dimensional assembly of elements that are in the form of flat or curved surfaces. The most common types of space structures are double layer grids, domes and barrel vaults. The individual members may be made of rolled, extruded or fabricated sections. The joints of the structures are mostly prefabricated in various forms and the designer must carefully select the type and the appropriate number of connectors. These structures provide a unique solution to cover large column free areas such as exhibition halls, airport hangers, conference halls, industrial buildings, etc., and selecting the number and the position of the columns are important issues. Double layer space structures are usually highly indeterminate and therefore have a large number of redundant members. It is important to choose the appropriate number of elements and joints for the structure under consideration [1,2,3].

Optimum shape design of space structures is the aim of the present work and to achieve an optimal configuration, parameters such as the number of joints, number of members, support conditions and the overall shape of the structures are considered. To achieve the optimal shape, the genetic algorithm with some modification is used. To reduce the length of the chromosome and to achieve a practical configuration, the existence of the joints of the structures and the locations of the columns are taken as the shape design variable as well as the cross-sectional areas of the elements of the structures under consideration. In addition for dome structures, the shape of the overall surface is considered unknown.

To begin with, a configuration with all possible members, joints, columns and surface shape is chosen. The existence of the joints and columns are formulated in the chromosome as zero (0) or one (1) bit. The zero bit indicates that the joint should be removed and thus all the members connected to that joint should also be removed. The same idea is employed for all the columns. As far as the shape of the curved surfaces is considered, a polynomial of up to the third order with unknown coefficients is chosen. Then these coefficients are selected by genetic algorithm such that the weight of the structure is minimal. Each of the generated configurations (chromosome) in the genetic algorithm population is checked for stability. The symmetry of the joints and support locations are also preserved for practical purposes. Thus the chromosome corresponding to each configuration, contains bits as many as the number of joints and columns and additional bits required for the cross sectional areas and the unknowns for the chosen surface.

The objective function is considered as the cost of members, joints, columns and cladding. For the top layer when a joint is removed, the arrangements of purlins and thus the cost of cladding will change. The design constraints include limits on member stresses, displacements and slenderness ratios of the members. The external loading conditions include dead, live and wind loads as required by the design codes.

With the proposed method, a number of double layer grids and domes are optimised. The resulting configurations are very interesting after the removal of unnecessary joints and columns. It was also observed that a part of sphere might not be appropriate for the dome structures as usually chosen by the designers. Second or third order polynomials would be more suitable for the shape of these structures. In the paper, the details of the approach including the method of shape optimisation, stability problems, modification of genetic algorithm and numerical results are presented.

1

M. Mashyekhi, "Optimum Shape Design of Double Layer Grids by Genetic Algorithm", M.Sc. Dissertation, Department of Civil Engineering, University of Kerman, Iran, 2004.

2

M. Kaykha, "Optimum Geometry Design of Braced Domes by Genetic Algorithm", M.Sc. Dissertation, Department of Civil Engineering, University of Kerman, Iran, 2004.

3

M. Khatibinia, "Optimum Configuration Design and Support Location of Domes by Genetic Algorithm", M.Sc. Dissertation, Department of Civil Engineering, University of Kerman, Iran, 2004.

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