Topology optimization of elastic continua using restriction

By Thomas Borrvall. 2001

138 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/b853c93b324db8caf809820568091f383171ebf4

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Topology optimization of continuum structures with material failure constraints (2004, background): “Work was also published simultaneously by Borrvall (2001) , in which the former penalization is found, and a complete theoretical and numerical discussion about this issue is given.”
Volume preserving nonlinear density filter based on heaviside functions (2010, methodology): “Before long, slope constraint method appeared (Bendsoe 1995; Petersson and Sigmund 1998; Borrvall 2001; Zhou et al. 2001).”
An adaptive multilevel approach to the minimal compliance problem in topology optimization (2005, methodology): “In fact |S(ρ)(x)− ρ(x)| ∈ [0, 1− ρ], since S(ρ)(x) ∈ [ρ, 1] for x ∈ Ω (see Borrvall and Petersson [6]).”
Topology optimization approaches (2013, background): “Experiments in Borrvall (2001) show mesh-independence for all values of q and demonstrate how increasing q-norms result in more and more grey transition regions between solid and void regions.”
Topology optimization in B-spline space (2013, background): “One type of restriction approaches is to impose constraints on the design space and this includes bounds on the design gradients [5], slope constraints [6], and constraints on perimeters [7].”
A reevaluation of the SIMP method with filtering and an alternative formulation for solid–void topology optimization (2005, methodology): “2001), regularized density control (Borrvall and Petersson 2001), MOLE method (Poulsen 2003), or by blurring filters (Sigmund 1994). For a good comparison between various restriction methods, refer to Borrvall (2001). The most prevalent approach in the literature is to filter the sensitivities (Sigm”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “However, since that time extensions have been proposed to some methods including global gradient (Borrvall 2001), slope control (Schury et al. 2012), local gradient control (Zhou et al. 2001), and regularized penalty methods (Borrvall and Petersson 2001b).”
Topology Optimization for Additive Manufacturing (2016, methodology): “1–22. Vora, P, Derguti, F, Mumtaz, K, Todd, I, and Hopkinson, N (2013). “Investigating a SemiSolid Processing technique using metal powder bed Additive Manufacturing Processes”.”
A mass constraint formulation for structural topology optimization with multiphase materials (2011, methodology): “Until now, a variety of techniques have been introduced, such as the perimeter control [20, 21] and its variant [5, 6], the density slope control [22, 23] and the filtering technique [24, 25].”
Morphology-based black and white filters for topology optimization (2007, background): “…2001); 2) constraint methods such as perimeter control (Ambrosio and Buttazzo, 1993; Haber et al, 1994), global gradient control (Bendsøe, 1995; Borrvall, 2001), local gradient control (Niordson, 1983; Petersson and Sigmund, 1998; Zhou et al, 2001), regularized penalty methods (Borrvall…”
A simple scheme to prevent checkerboard patterns and one-node connected hinges in topology optimization (2002, background): “Note also that Borrvall has shown examples indicating that a restriction of the H 2 norm of the design may be used to suppress the 1-node connected hinges ( Borrvall 2001 ).”