Composite Shaft Optimization Using Simulated Annealing, Part I: Natural Frequency

Abstract

In this study a fiber-reinforced composite shaft design is optimized. The optimization procedure is carried out in two stages. First, the shaft natural frequency is maximized with the constraint imposed on the shaft buckling torque and torsional strength. In the second stage of optimization, shaft weight is minimized with the constraint imposed on the natural frequency obtained from the first stage, shaft buckling torque and torsional strength. Shafts of uniform layup and uniform wall thickness (UU), uniform fiber layup and variable wall thickness (UV), variable fiber layup and uniform wall thickness (VU) and variable fiber layup and variable wall thickness (VV) have been considered. The shaft is modelled as a simply supported Timoshenko beam in which shear deformation, rotary inertia and gyroscopic effects are included. Rayleigh-Ritz displacement are used for deriving the solution equation. A Simulated Annealing (SA) global optimization routine is used. Although this routine requires large number of function evaluations to find the optimum solution, it finds the global optimum with high probability even for ill conditioning functions with numerous local minima.