On the validity of using small positive lower bounds on design variables in discrete topology optimization

It is proved that an optimal {ε, 1} ⁿ solution to a “ε-perturbed” discrete minimum weight problem with constraints on compliance, von Mises stresses and strain energy densities, is optimal, after rounding to {0, 1} ⁿ , to the corresponding “unperturbed” discrete problem, provided that the constraints in the perturbed problem are carefully defined and ε > 0 is sufficiently small.