OPTIMUM DESIGN OF STRUCTURES WITH FREQUENCY CONSTRAINTS

An efficient method is presented for optimum design of structures subject to stress, displacement and frequency constraints. The design variables are the actual dimensions of the cross-sectional areas of the members. The design variables can be considered as continuous or discrete variables. To reduce the computational cost of optimization, the structural response quantities such as member forces, displacements and eigenvalues are approximated in terms of some intermediate variables. Thus the analysis of the structure is not required in each design cycle. A new approach is developed in the present study to approximate the eigenvalues. All the quantities in the Rayleigh quotient such as eigenvector, stiffness and mass matrices are approximated separately and then the approximate eigenvector is recovered. The design sensitivity analysis is performed analytically. The continuous-discrete optimization is carried out by using duality theory. A planar grillage is solved and the results are presented to check the efficiency of the approach.