  In topology optimization, the treatment of stress constraints for very large
scale problems has so far not been tractable due to the failure of robust
agglomeration methods, i.e. their inability to accurately handle the locality
of the stress constraints. This paper presents a three-dimensional design
methodology that alleviates this shortcoming using both deterministic and
robust problem formulations. The robust formulation, based on the three-field
density projection approach, is extended to handle manufacturing uncertainty in
three-dimensional stress-constrained problems. Several numerical examples are
solved and further post-processed with body-fitted meshes using commercial
software. The numerical investigations demonstrate that: (1) the employed
solution approach based on the augmented Lagrangian method is able to handle
large problems, with hundreds of millions of stress constraints; (2) if
appropriate interpolation parameters are adopted, voxel-based (fixed grid)
models can be used to compute von Mises stresses with excellent accuracy; and
(3) in order to ensure manufacturing tolerance in three-dimensional
stress-constrained topology optimization, a combination of double filtering and
more than three realizations may be required.
