This paper presents an improved optimality criteria (OC) method for minimum-weight design of bar structures supporting non-structural mass and subjected to multiple natural frequency constraints and minimum gauge restrictions. The convergence quality of the OC method hinges on both the number of active constraints retained and the choice of a proper step size. This being the case, a criterion, which uses previous scaled designs to 'adaptively' tune the step size, is established with the purpose of dissolving the (sometimes violent) oscillations of scaled design weights in the iteration history. As the step size is tuned, the convergence rate is decreased. Hence, a modified Aitken's accelerator, which extrapolates from previous scaled designs to obtain an improved one, is used. Its effect is to both increase the overall rate and reduce the net cost of convergence by reducing the number of repeat finite element analyses. The method presented here is used to qualitatively survey the convergence of several OC recursive schemes compositely used to resize and to evaluate the Lagrange multipliers. Design examples are presented to demonstrate the method. The method is adaptable, as it eliminates the need for adjustments of internal parameters during the redesign stage.
Weight optimization of large space frames under dynamic constraints requires adaptable design search techniques because of the enormous number of sizing variables, the highly nonlinear frequency constraint surfaces, and the multiple points of local minima. With modern OC procedures, based on alternately satisfying the constraints (scaling) and applying the Kuhn-Tucker (optimality) condition (resizing), the convergence to weight minima is oftentimes oscillatory. Even though the convergence rate for OC methods is initially fast, it gradually slows near local extrema, mainly because the selection of appropriate step sizes (or move limits) in the redesign phase becomes increasingly difficult. The focus here is to create specific criteria based on past scaled designs to *'damp out" the oscillatory convergence propensity of OC recursive methods. Several OC recursive strategies, which are frequently worked to resize and to evaluate the Lagrange multipliers, are steered by the present approach to design large space frames under multiple dynamic constraints. Besides this, the design iteration histories obtained by the various recursive strategies are compared graphically. On the whole, the present OC approach achieves a smooth upper-bound convergence to weight minima, as it quickly dissolves the (sometimes violent) oscillations of scaled weights in the iteration history. Most of all, the method eliminates the need for adjustments of internal parameters during the redesign phase.
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