Adaptable optimality criterion techniques for large-scale space frames with multiple frequency constraints

This paper presents an adaptive optimality criteria (OC) approach for frequency-constrained weight minimization of large-scale space frames supporting nonstructural mass and subjected to minimum and maximum gauge restrictions. The iterative procedure 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 (i.e., two principal moments of inertia and a torsional constant) are uniformly scaled to the constraint surfaces using a closed-form formulation. The closed-form scaling procedure is united with an adaptable redesign strategy in which linear extrapolates of past scaled design vectors are coupled with automatically tuned OC recursive formulae. Several practical design examples are presented to demonstrate the method. On the average, the method achieves a smooth 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.