Keywords: structural optimization, multiobjective optimization, reliability analysis, trusses, evolutionary algorithms.

In this work the influence of including buckling constraints in the multiobjective optimization of truss structures for minimum weight and maximal reliability is examined. Uncertainties in structural loading and material properties are included in the structural analysis and an evolutionary algorithm is deployed in the identification of the non-dominated solution front. To account for the high cost of analysis in a nondeterministic problem formulation, a fast and efficient approach to compute the system reliability index for complex bar structures based on the reliability indices of individual bar components is used in the system reliability computation. The focus of the work is on determining how the inclusion of elastic buckling influences the front of non-dominated solutions in bar structures. A simple classical test case of a six bar sized and first-degree redundant truss is used in all numerical experiments. The NSGA-II algorithm is used with uniform mutation rate and binary gray codification.

Results show that the quality of the non-dominated design set seems unaffected by the introduction of buckling considerations; nevertheless, a lesser number of solutions are located on the optimal front. The quality of solutions is similar in the final non-dominated designs, with and without considering buckling optimization. From the best non-dominated designs, it is possible to infer that structural solutions are achieved of the same quality in terms of reliability and low weight by explicit inclusion of the buckling failure. From the designer's point of view, and according to the accumulated front figures, the solution qualities achieved are of similar performance, although the buckling case has a lower size-set of solutions. The S-metric or hypervolume outcomes show that their average and best values during the evolution are better in the no buckling case, and the standard deviation is also lower. Including the buckling failure produces lower hypervolume averages, best and accumulated front values, and greater standard deviation, (all worse values than the no buckling case); this lower value results from the lower number of points belonging to the final non-dominated front, but not to the quality of the final solutions.

The limited experimentation points out that the quality of the solutions is not affected by the inclusion of the buckling failure mode. The numbers of final designs on the non-dominated solution front however, diminish with the inclusion of this mode of failure.

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