Minimization of weight in truss structures under probabilistic constrains

The main purpose of the reliability theory of structural systems is the optimal design based on the reliability concept. Trusses and space structures are widely used, and cost and safety both are important in these structures. Therefore the weight optimization of these structures based on the theory of reliability (probabilistic optimization) using Genetic Algorithms was studied in this paper. The objective function was weight of structure and the constraints were based on the failure probability of elements or nodes or the system. To increase the accuracy of structural safety calculations, the probabilistic form of buckling is presented in this research. The results of this study show that increasing the system allowable failure probability decreases the optimum weight of structure. The process of this weight loss occurred at first with a very fast slope and then with a gentle slope and finally tended to a constant value. Optimum weight was very sensitive to coefficient of variation comparison of allowable failure probability. In the probabilistic optimization, if the system allowable failure probability and coefficient of variation of load and yield stress are considered near zero, and if results are compared to the deterministic optimization, the difference in optimum weight is less than 9%. In this case, convergence for deterministic optimization was very fast and occurred in less than 20 generations but convergence in probabilistic optimization occurred slowly after 85 generations.