Topology optimization of beam cross sections

Perhaps, this paper reports the ®rst successful applications of the topology optimization in the design of (thin- walled) beam sections. In particular, topologically di€erent thin-walled beam cross sections can be obtained by the present approach, which is very useful in identifying the direction and location of sti€eners. In formulating the topology optimization problems, a simple power law is used for the relation between the density of an element with a hole and the mechanical properties of the element. The sensitivity of the torsional rigidity is obtained by developing a ®nite element model of a St. Venant torsion problem, and the Euler beam theory is used for the sensitivity analysis of the bending rigiditie