An extrapolation approach for the solution of singular optima

In this paper, an efficient extrapolation approach for the solutions of singular problems in structural topology optimization. subjected to stress constraints is presented. On the basis of the epsilon-relaxed formulation recently proposed by the authors, the sensitivities of the active design variables and the Lagrange multipliers associated with the active constraints with respect to the relaxation parameter at the current optimum of the relaxed problem are derived. Through the use of these sensitivities, a singular optimum can be obtained by employing the extrapolation technique at a relatively large value of epsilon, thus great computation efforts associated with the continuation approach for the solution of singular optimum can be saved. Several numerical examples illustrate the effectiveness of the proposed approach.