Truss Topology Optimization via Zero-One (Binary) Programming

In this paper, a new method has been proposed for the topology optimization of trusses. The method takes advantage of the equation of equilibrium between internal and external forces in the flexibility method of structural analysis. The internal forces are written as the multiplication of cross-sections of members into their stresses. The stress constraints (i.e. limits on the stress values) are then imposed on the problem and eventually, the topology optimization of trusses ends up in a Linear Programming (LP) problem. The solution to the LP problem is straightforward and results in a global optimum. Accordingly, the outcome of our formulation is a global optimum.When the displacement constraints are included among the constraints, the truss topology optimization turns into a nonlinear optimization problem. To convert the problem to a linear programming problem, we used discrete design variables and converted the problem to a binary (zero-one) integer programming. Several examples were solved and compared to the published examples in the literature. It was observed that our method of truss topology optimization ends up with the same results as the previous research works, but with much less calculations. Nevertheless, our results are proved to be the global optimum, whereas the methods used in the literature cannot prove their global optimality