Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Revisiting element removal for density-based structural topology
  optimization with reintroduction by Heaviside projection   We present a strategy grounded in the element removal idea of Bruns and
Tortorelli [1] and aimed at reducing computational cost and circumventing
potential numerical instabilities of density-based topology optimization. The
design variables and the relative densities are both represented on a fixed,
uniform finite element grid, and linked through filtering and Heaviside
projection. The regions in the analysis domain where the relative density is
below a specified threshold are removed from the forward analysis and replaced
by fictitious nodal boundary conditions. This brings a progressive cut of the
computational cost as the optimization proceeds and helps to mitigate numerical
instabilities associated with low-density regions. Removed regions can be
readily reintroduced since all the design variables remain active and are
modeled in the formal sensitivity analysis. A key feature of the proposed
approach is that the Heaviside functions promote material reintroduction along
the structural boundaries by amplifying the magnitude of the sensitivities
inside the filter reach. Several 2D and 3D structural topology optimization
examples are presented, including linear and nonlinear compliance minimization,
the design of a force inverter, and frequency and buckling load maximization.
The approach is shown to be effective at producing optimized designs equivalent
or nearly equivalent to those obtained without the element removal, while
providing remarkable computational savings.

11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con