A primal-dual approach in truss topology optimization

The objective of truss topology optimization is to find, for a given weight, 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 single load case and without bounds on bar volumes, the problem can be written as a linear programming problem with nodal displacements as variables. The addition to the objective function of a quadratic term vanishing at the optimum allows us to use a dual solution scheme. A conjugate gradient method is well suited to maximize the dual function. Several 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 obtaining a sufficient number of possible directions. Some examples taken from the literature are treated to illustrate the quality of the solution and the influence of initial topology. (C) 1997 Civil-Comp Ltd and Elsevier Science Ltd.