Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytical relationships for imposing minimum length scale in the robust
  Topology Optimization formulation   The robust topology optimization formulation that introduces the eroded and
dilated versions of the design has gained increasing popularity in recent
years, mainly because of its ability to produce designs satisfying a minimum
length scale. Despite its success in various topology optimization fields, the
robust formulation presents some drawbacks. This paper addresses one in
particular, which concerns the imposition of the minimum length scale. In the
density framework, the minimum size of the solid and void phases must be
imposed implicitly through the parameters that define the density filter and
the smoothed Heaviside projection. Finding these parameters can be time
consuming and cumbersome, hindering a general code implementation of the robust
formulation. Motivated by this issue, in this article we provide analytical
expressions that explicitly relate the minimum length scale and the parameters
that define it. The expressions are validated on a density-based framework. To
facilitate the reproduction of results, MATLAB codes are provided.
  As a side finding, this paper shows that to obtain simultaneous control over
the minimum size of the solid and void phases, it is necessary to involve the 3
fields (eroded, intermediate and dilated) in the topology optimization problem.
Therefore, for the compliance minimization problem subject to a volume
restriction, the intermediate and dilated designs can be excluded from the
objective function, but the volume restriction has to be applied to the dilated
design in order to involve all 3 designs in the formulation.

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The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
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The categories of this paper are: eess
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas