  Lattice-like structures can provide a combination of high stiffness with
light weight that is useful in many applications, but a resolved finite element
mesh of such structures results in a computationally expensive discretization.
This computational expense may be particularly burdensome in many-query
applications, such as optimization. We develop a stress-constrained topology
optimization method for lattice-like structures that uses component-wise
reduced order models as a cheap surrogate, providing accurate computation of
stress fields while greatly reducing run time relative to a full order model.
We demonstrate the ability of our method to produce large reductions in mass
while respecting a constraint on the maximum stress in a pair of test problems.
The ROM methodology provides a speedup of about 150x in forward solves compared
to full order static condensation and provides a relative error of less than 5%
in the relaxed stress.
