Keywords: genetic algorithm, truss, topology, structural optimisation.

This paper focuses on the application of genetic algorithms (GAs) to structural optimisation problems by simultaneously varying member size, truss topology and configuration. The classic ten bar redundant truss problem has been used as a test case. In the first instance, only member size and topology were considered as design variables. In the second case, configuration was introduced as an additional design variable.

The genetic algorithm (GA) designed for this study employs a combination of q-ary and floating point representations. The q-ary representation is used to represent the discrete member sizes while the floating point representation is used to represent continuous node positions.

Structural analysis was conducted using the stiffness method. A node to node stability check was used to identify unstable, infeasible truss structures which were then severely penalised in the GA fitness evaluation.

When considering the truss optimisation with variable member size and topology, the best result achieved by the GA was 2333.31kg. This compares reasonably with the results from the literature (Deb and Gulati 2222.3kg [1], Nanakorn and Meesomklin 2250.8kg [2] and Rajeev and Krishnamoorthy 2234.3kg [3]). However the GA was unable to produce results as good as those from the literature. This can be attributed to the fact that the GA failed to find the 6 bar topology (believed to be optimal). The probability of a member being null was increased by introducing an additional 41 alleles representing absent members. Once the 84-ary representation was applied, the GA was able to locate the optimal 6 bar topology, and produced a best truss mass.

When considering the truss optimisation with variable member size and topology, the best result achieved by the GA was 2147.13kg. The results compare well with those from the literature, (Rajeev and Krishnamoorthy [3] 2192.0kg). Again the GA failed to identify the 6 bar topology as a possible solution, so the optimisation was repeated using the 84-ary representation (allowing 42 null members). The best solution located was 2176.50kg, which did not correspond to the 6 bar topology, however the 6 bar topology was identified as optimal in two out of 20 runs of the GA, within 20kg of the best result produced.

Where node coordinates are included as variables, there is little difference in the quality of the solutions produced by the 43-ary and 84-ary representations. This suggests that null member probability is less critical in the optimisation of trusses when member size, topology and configuration are all considered as design variables. The GA was able to identify a number of different topology and configuration combinations that provide near optimal solutions. This highlights one of the advantages of the GA, its ability to identify possible structural solutions that may not have been considered when using conventional design methods.

1

K. Deb and S. Gulati, "Design of truss-structures for minimum weight using genetic algorithms", Finite Elements in Analysis and Design, vol. 37, pp. 447-465, 2001. doi:10.1016/S0168-874X(00)00057-3

2

P. Nanakorn and K. Meesomklin, "An adaptive penalty function in genetic algorithms for structural design optimization", Computers and Structures, vol. 79, pp. 2527-2539, 2001. doi:10.1016/S0045-7949(01)00137-7

3

S. Rajeev and C.S. Krishnamoorthy, "Genetic algorithms-based methodologies for design optimization of trusses", Journal of Structural Engineering, pp. 350-358, 1997. doi:10.1061/(ASCE)0733-9445(1997)123:3(350)

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