An adaptive procedure for stabilizing convergence quality in frequency‐constrained design optimization of bar structures supporting non‐structural mass

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 descreased. 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 demonstrat the method. The method is adaptable, as it eliminates the need for adjustments of internal parameters during the redesign stage.