Keywords: dome structures, optimization, geometrically nonlinear design, particle swarm, ant colony, hybrid.

Covering large areas without intermediate supports has always been an attractive problem for architects and a challenging task for structural engineers. Latticed domes are lightweight and elegant structures that provide cost-effective solutions to cover such large areas. The algorithm presented in this study carries out the optimum topological design of lattice domes. The serviceability and strength requirements are considered in the design problem as specified in LRFD-AISC. The algorithm takes into account the nonlinear response of the dome due to the effect of axial forces on the flexural stiffness of members. Furthermore, an overall stability check is also necessary during the analysis to ensure that the structure does not lose its load carrying capacity due to instability. The elastic stability analysis of domes involves repeated analysis of the structure using the stiffness method at progressively increasing load factors. At each increment of the load factor, nonlinear analysis of the structure is carried out. During the nonlinear analysis iteration, the determinant of the overall stiffness matrix is checked to determine whether at any load increment it becomes negative. This is an indication of a loss of stability in the structure and the load factor which causes this, is identified as the critical load factor.

The optimum solution of the design problem is obtained using a hybrid algorithm, called particle swarm ant colony optimization (PSACO). In this approach, the particle swarm optimization with passive congregation algorithm (PSOPC) is combined with the ant colony algorithm. PSACO applies the particle swarm optimizer with passive congregation for global optimization and ant colony approach is employed as a local search in which ants apply a pheromone-guided mechanism to update the positions found by the particles in the earlier stages. This paper utilizes a discrete version of the particle swarm ant colony optimization approach (DPSACO) for the design of dome structures. In this method, particles (or ants) are allowed to select discrete values from the permissible list of cross sections. Similar to PSACO, the DPSACO prevents the solution to become trapped in the local optimums by using the PSOPC algorithm for global optimization, and the ant colony approach is employed as a local search. Also, for the velocity of particles, a new formula is used to improve the performance of the present method.

The optimum design algorithm presented here determines the total number of rings, the optimum height and the optimum steel section designations for the members of single layer latticed dome from the available steel pipe section table and implements the design constraints from LRFD-AISC. The results obtained showed that the DPSACO method is a robust technique which can successfully be used for the optimum topology design of domes.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £78 +P&P)