Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topology optimization with worst-case handling of material uncertainties   In this article a topology optimization method is developed, which is aware
of material uncertainties. The uncertainties are handled in a worst-case sense,
i.e. the worst possible material distribution over a given uncertainty set is
taken into account for each topology. The worst-case approach leads to a
minimax problem, which is analyzed throughout the paper. A conservative convex
relaxation for the inner maximization problem is suggested, which allows to
treat the minimax problem by minimization of an optimal value function. A
Tikhonov type and a barrier regularization scheme are developed, which render
the resulting minimization problem continuously differentiable. The barrier
regularization scheme turns out to be more suitable for the practical solution
of the problem, as it can be closely linked to a highly efficient interior
point approach used for the evaluation of the optimal value function and its
gradient. Based on this, the outer minimization problem can be approached by a
gradient based optimization solver like the method of moving asymptotes.
Examples from additive manufacturing as well as material degradation are
examined, demonstrating the practical applicability as well as the efficiency
of the suggested method. Finally, the impact of the convex relaxation of the
inner problem is investigated. It is observed that for large material
deviations, the robust solution may become too conservative. As a remedy, a
RAMP-type continuation scheme for the inner problem is suggested and
numerically tested.

9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci