Multi-objective optimization of ring stiffened cylindrical shells using a genetic algorithm

In this paper, the genetic algorithm (GA) method is used for the multi-objective optimization of ring stiffened cylindrical shells. The objective functions seek the maximum fundamental frequency and minimum structural weight of the shell subjected to four constraints including the fundamental frequency, the structural weight, the axial buckling load, and the radial buckling load. The optimization process contains six design variables including the shell thickness, the number of stiffeners, the width and height of stiffeners, the stiffeners eccentricity distribution order, and the stiffeners spacing distribution order. The real coding scheme is used for representing the solution string, while the generation number-based adaptive penalty function is applied for penalizing infeasible solutions. In analytical solution, the Ritz method is applied and the stiffeners are treated as discrete elements. Some examples of simply supported cylindrical shells with nonuniform eccentricity distribution and nonuniform rings spacing distribution are provided to demonstrate the optimality of the solution obtained by the GA technique. The effects of objective weighting coefficients and bounding values of the design variables on the optimum solution are studied for various cases. The results show that the optimal solution can vary with the weighting coefficients significantly. It is also found that extreme reduction and augmentation in turn in the structural weight and fundamental frequency can be simultaneously achieved by selecting suitable stiffeners’ geometrical parameters and distributions. Furthermore, the bounding values of the design variables have great effects on the optimum results.