Topology optimization of beam cross sections

Perhaps, this paper reports the first successful applications of the topology optimization in the design of (thin-walled) beam sections. In particular, topologically different thin-walled beam cross sections can be obtained by the present approach, which is very useful in identifying the direction and location of stiffeners. 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 finite element model of a St. Venant torsion problem, and the Euler beam theory is used for the sensitivity analysis of the bending rigidities. (C) 1999 Elsevier Science Ltd. All rights reserved.