Optimum geometry design of nonlinear braced domes using genetic algorithm

Domes are lightweight and cost effective structures that are used to cover large areas. They are mainly comprised of a complex network of triangles made out of slender members. The behaviour of flexible dome is nonlinear under the external loads which makes it necessary to consider the geometrical non-linearity in their analysis to obtain realistic response of these structures. Furthermore, instability check during the nonlinear analysis is of prime importance. In this paper, an algorithm is presented for the optimum geometry design of nonlinear braced domes. The height of crown is taken as design variable in addition to the cross-sectional properties of members. A procedure is developed that calculates the joint coordinates automatically for a given height of the crown. The optimum design algorithm takes into account the nonlinear response of the dome due to the effect of axial forces on the flexural stiffnesses of members. It considers serviceability requirements as well as combined strength limitations set by BS 5950. The solution of the design problem is obtained by genetic algorithm. The elastic instability analysis is then carried out for each individual in the initial population until the ultimate load factor is reached. During this analysis, checks on the overall stability of the dome is conducted. If the loss of stability takes place, this individual is taken out of the population and replaced by a new randomly generated individual. This replacement policy is repeated until an individual is found which does not have instability problem. Once the initial population is established where all the individuals are free of instability problem, the regular genetic operations are applied to generate a new population. Number of design examples are included to demonstrate the application of the algorithm.