Optimum design of steel space frames with frequency constraints using three point Rayleigh quotient approximation

Abstract Optimum design of steel structures is achieved with frequency constraints. To reduce the number of required frequency analysis in the optimization process, the frequencies are approximated in each design cycle. A three point approximation is developed to approximate the frequencies. The method is based on the creation of a second order approximation with Hessian matrix containing only the diagonal terms. The elements of the Hessian matrix are estimated from the information available from the previous iterations. The effect of the higher order terms of the Taylor series expansion is also considered. It is shown that this approach creates high quality approximation of the frequencies. Examples are solved and the results are compared with published work.