Topology optimization using regularized intermediate density control

By Thomas Borrvall, Joakim Petersson. 2001

216 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/5309f43418d5ea4a53a585d8bb439886ced5ab24

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Honeycomb Wachspress finite elements for structural topology optimization (2009, methodology): “Other methods that address the mesh-dependency problem include the perimeter control (Ambrosio and Buttazzo 1993; Haber et al. 1996), density and sensitivity filters (Bruns 2005; Wang and Wang 2005), monotonicitybased method (Poulsen 2003), regularized density control ( Borrvall and Petersson 2001b ”
An alternative interpolation scheme for minimum compliance topology optimization (2001, background): “Haber et al. 1996; Allaire and Francfort 1993; Allaire and Kohn 1993; Borrvall and Petersson 2001 ).”
Modelling topology optimization problems as linear mixed 0–1 programs (2003, background): “One method is to enforce and upper bound on the perimeter (the length of the boundary of the structure) of the structure, see e.g. Haber et al. [1] and Petersson [2].”
A simple scheme to prevent checkerboard patterns and one-node connected hinges in topology optimization (2002, background): “The checkerboard problem is well understood (Jog and Haber 1996; D´ iaz and Sigmund 1995) and there already exists several ways to solve it, see Sigmund and Petersson (1998), Borrvall and Petersson (2001) , Poulsen (2002) and references therein.”
Topology optimization in B-spline space (2013, methodology): “The other type of restriction includes the use of filters and penalty: sensitivity filters from Sigmund [8, 9], density filter [10, 11], regularized penalty [12], and Tikhonov-type regularization [13].”
A reevaluation of the SIMP method with filtering and an alternative formulation for solid–void topology optimization (2005, methodology): “…University of Illinois at Urbana–Champaign, Urbana, IL, 61801, USA e-mail: tbruns@uiuc.edu design variable bounds that impose density slope constraints (Zhou et al. 2001), regularized density control (Borrvall and Petersson 2001), MOLE method (Poulsen 2003), or by blurring filters (Sigmund 1994).”
Optimal topologies derived from a phase-field method (2012, background): “Bruns and Tortorelli 2001; Borrvall and Petersson 2001 ).”
Morphology-based black and white filters for topology optimization (2007, methodology): “Restriction methods for density based topology optimization problems can roughly be divided into three categories: 1) mesh-independent filtering methods, constituting sensitivity filters (Sigmund, 1994, 1997; Sigmund and Petersson, 1998) and density filters (Bruns and Tortorelli, 2001; Bourdin, 2001”
Topology optimization in crashworthiness design (2006, background): “There are also other mathematical problems associated with this optimization technique, e.g., checkerboard patterns and mesh dependency.Theseissuesarediscussedin,e.g.,Sigmundand Petersson (1998), Petersson (1998), Borrvall and Petersson (2001) , and Bendsoe and Sigmund (2003).”