Optimization of Rigid Steel Frames Using Direct Analysis and Improved Differential Evolution Considering Frequency Constraints

In this paper, the authors present an optimization problem of nonlinear inelastic rigid steel frames that considers both load combinations and frequency constraints for the first time. Direct analysis-based on the beam–column approach is employed to account for the non-geometric and nonlinear behaviors of the structure. The objective function is the total cost of the structure which is simplified as a function of total weight. The constraints of the optimization include the strength and serviceability conditions, and structural frequency requirements. An improved differential evolution algorithm is employed to solve the proposed optimization problem that effectively reduces the number of structural analyses. A three-bay five-story planar frame is studied to illustrate this work. The numerical results show that the optimization design of structures considering both load combinations and structural frequency constraints improves the performance of the structure. Furthermore, the proposed optimization problem was more complicated than the optimization problem without considering structural frequency constraints.