Optimum design of structures with high-quality approximation of frequency constraints

Abstract

Optimum design of structures is achieved with multiple frequency constraints. A two-point approximation is employed to approximate the frequencies. Thus, in the specified move limits, the eigenvalue analysis of the structure is not required. To enhance the quality of approximation, the Rayleigh quotient is approximated in terms of some intermediate variables, using the two-point approximation. The analytical derivatives of the eigenvalues are used in the design process. Examples are offered and the results are compared with previous work.