A PRIMAL-DUAL APPROACH IN TRUSS TOPOLOGY OPTIMIZATION

The objective of truss topology optimization is to find, for a given w eight, the stiffest truss, defined as a subset of an initially choosen set of bars called the ground structure. The restrictions are bounds on bar volumes and the satisfaction of equilibrium equations. For a si ngle load case and without bounds on bar volumes, the problem can be w ritten as a linear programming problem with nodal displacements as var iables. The addition to the objective function of a quadratic term van ishing at the optimum allows us to use a dual solution scheme. A conju gate gradient method is well suited to maximize the dual function. Sev eral ground structures are introduced. For large networks, those where each node is connected to those situated in a certain vicinity give a good compromise between generating a reasonable number of bars and ob taining a sufficient number of possible directions. Some examples take n from the literature are treated to illustrate the quality of the sol ution and the influence of initial topology. (C) 1997 Civil-Comp Ltd a nd Elsevier Science Ltd.