Frequency-constrained optimization of space frames having general cross-sectional relationships∗

Abstract

Abstract An optimality criteria (OC) method is presented for weight optimization of space frames having general cross-sectional relationships. The space frames support a sizeable amount of non-structural mass, while multiple natural frequency constraints, and minimum and maximum gauge restrictions are imposed on their design. The iterative design method involves alternately satisfying the constraints (scaling) and applying the Kuhn-Tucker (optimality) condition (resizing). The primary sizing variables (cross-sectional areas), and indirectly the secondary ones (two principal moments of inertia and a torsional constant), are uniformly scaled to the constraint surfaces using a nonlinear closed-form formulation. No exact scaling formulation for this class of problem has been proposed and tested in the optimization literature hitherto. The closed-form scaling procedure is united with an adaptable design strategy in which linear extrapolates of past-scaled design vectors are coupled with automatically-tuned OC recursive methods. Elementary design examples are presented to demonstrate the method. On average, the method achieves a stable upper-bound convergence of weight minima, as it quickly dissolves the (sometimes violent) oscillations of scaled weights in the iteration history. Most of all, the present design strategy eliminates the need for adjustments of internal parameters during the redesign phase.