Fuzzy Approach for Optimization of Cold-Formed Cross Sections

This paper presents a fuzzy procedure for obtaining optimal design of channel section shapes under bending moment. The proposed approach refers to an ideal, equivalent single objective representation for the bicriteria objectives, where the cross-sectional area of thin-walled beam is the first objective, while the deflection of the beam is the second one. The design variables were selected as the geometric parameters of cross section. The set of constraints includes global and stability conditions and the strength condition. The membership functions for each objective are constructed and by the proposed formulation, the bicriteria problem will be transformed to an ideal equivalent single problem. By the proposed formulation for the equivalent objective, the best compromise solution is obtained. An illustrative example is presented and the results were discussed and compared with other approaches.