Optimal Linear Segmented Structures with Variable Segment Boundaries

Abstract

Recently, the writers and others considered the optimization of continuously linear segmented structures. This geometrical constraint has practical advantages in actual design problems from the viewpoints of fabrication and prevention of stress concentrations that occur in optimal solutions with sudden changes in the cross‐sectional area. So far in the studies, the segmental lengths of the structure are prescribed. The current work considers the segmented lengths to be unknown a priori and seeks to optimize them as well. A numerical method based on optimal control theory is proposed for the optimization exercise, and a simple beam problem is used to illustrate the validity and accuracy of the method.