We introduce a new relaxation scheme for structural topology optimization problems with local stress constraints based on a phase-field method. The starting point of the relaxation is a reformulation of the material problem involving linear and 0-1 constraints only. The 0-1 constraints are then relaxed and approximated by a Cahn-Hilliard type penalty in the objective functional, which yields convergence of minimizers to 0-1 designs as the penalty parameter decreases to zero. A major advantage of this kind of relaxation opposed to standard approaches is a uniform constraint qualification that is satisfied for any positive value of the penalization parameter.
The relaxation scheme yields a large-scale optimization problem with a high number of linear inequality constraints. We discretize the problem by finite elements and solve the arising finite-dimensional programming problems by a primal-dual interior point method. Numerical experiments for problems with stress constraints based on different criteria indicate the success and robustness of the new approach.

@Article{BS06,
  author       = {Burger, M. and Stainko, R.},
  title        = {Phase-field relaxation of topology optimization with local stress constraints,},
  journal      = {SIAM J. Control. Optim.},
  volume       = {45},
  pages        = {1447-1466},
  year         = {2006},
  url          = \{/2006/BS06},
}