On the trajectories of the epsilon-relaxation approach for stress-constrained truss topology optimization

We consider the nonconvex problem of minimizing the weight of a linearly elastic truss structure subject to stress constraints under multiple load conditions. The design variables are the cross-sectional areas of the elements, and the stress constraints are imposed only on elements with strictly positive areas. To avoid degenerate feasible domains, it has been suggested that the stress constraints of the original problem should be relaxed by a positive scalar ε, leading to the so-called ε-relaxed problem.