MULTIOBJECTIVE DESIGN OPTIMIZATION OF CONTINUOUS BEAMS BY NUMERICAL METHODS

The optimal thickness distribution of a two‐span continuous beam is determined with the objectives of minimizing the maximum stress, maximizing the fundamental frequency and frequency separation between adjacent frequencies. The self‐weight of the beam is included in the computations. The multiobjective design problem is solved by using the concept of Pareto optimality. The beam thickness is approximated by constant splines. The stress distribution and the frequencies are determined by the finite element method. The optimization of the beam is carried out by the feasible direction method and by employing a quadratic approximation of the thickness function. Numerical results are given for two‐objective design problems. Optimal trade‐off curves, thickness distributions and stress distributions of optimally designed beams are presented in graphical form. The effects of self‐weight and different design objectives on the thickness distribution are investigated.