Optimal design of damped structures under dynamic loads

Abstract

An algorithm for optimal design of damped elastic structures under dynamic loads is Presented and a computer program is developed. The structures are modeled by finite element method and the structural damping is included in terms of modal damping ratios. To obtain dynamic responses of damped structures, modal analysis technique is used. Dominant modal shapes and corresponding natural frequencies are obtained by a simultaneous iteration algorithm. In the optimal design formulation, constraints on stress, displacement and natural frequencies are considered. Loading to the structure is input by either dynamic forces or base accelerations. A generalized steepest descent method is utilized and combined with the dynamic structural analysis program. Several planar frame structurals are optimized as illustrative examples, using the computer program developed. Generally, the optimal shapes of structures under dynamic loads are found much different from those under static loads. And, the damping of structures has an effect to strenthen structures against impulsive loadings, so that more materials can be saved for a given dynamic loads if the damping is made larger.