On the convergence quality of minimum-weight design of large space frames under multiple dynamic constraints

Abstract

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.

Graph based discrete optimization in structural dynamics

“…McGee and Phan [5] considered space frames with relatively larger numbers of degrees of freedom and dynamic constraints. Their discussion, based on the Optimality Criteria approach, was devoted to the computational complexity of problems with constraints imposed on several natural frequencies.…”