Reliability-based multi-objective optimal design of spatial trusses using NSGA-II

This paper addresses a reliability-based multi-objective desgin method for spatial truss structures.The uncertainties of the applied load and the resistance of the truss members have been taken into account by generating a set of 50 random numbers. The failure probability of each truss member have been evaluated and consequently the failure probability of the entire truss system have been calculated considering as a series system. A multi-objective optimization problem has been defined with objective functions of truss weight and failure probability of the entire truss structure. The cross sectional area of the truss members have been considered as the design variables. The limitations of nodal displacements and allowable stress of the members have been defined as constraints. A 25-bar benchmark spatial truss has been considered as the case study structure and has been optimally designed using the non-dominated sorting genetic algorithm II (NSGA-II). The results show effectivness and simlicity of the proposed method which can provide a wide range of optimal solutions through Pareto fronts. These optimal solutions can provide both safety and reliability for the truss structure. Also, the results indicate that the failure probability of the truss structure reduces by increasing the uncertainty level of load and resistance.