Checkerboard and minimum member size control in topology optimization

By M. Zhou, Y. Shyy, H. Thomas. 2001

257 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/4a1d052491742410f1dcd689fa2bca3166da9238

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Shape optimization and its extension to topological design based on isogeometric analysis (2010, background): “, 1996), the slope constraint (Petersson and Sigmund, 1998; Borrvall, 2001; Zhou et al., 2001) and density redistribution (Youn and Park, 1997).”
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).”
A topology optimization method based on the level set method incorporating a fictitious interface energy (2010, methodology): “To mitigate these problems, a method using a perimeter constraint [42] and methods using a density gradient constraint [43,44] have been proposed.”
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 alternative interpolation scheme for minimum compliance topology optimization (2001, background): “Another approach is to introduce local gradient constraints on the variables defining the geometry, Petersson and Sigmund (1998) and references therein, Zhou et al. (1999) .”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “2012), local gradient control (Zhou et al. 2001), and regularized penalty methods (Borrvall and Petersson 2001b).”
Stress-based topology optimization for continua (2010, background): “Optistruct Filter ( Zhou et al. 2001 ) Not available Not available Min.”
A simple checkerboard suppression algorithm for evolutionary structural optimization (2001, methodology): “By relaxing the slope constraints of density function, Zhou et al. (2000, 2001) developed a density control algorithm into the commercial structural optimization package Altair OptiStruct.”
Study of key algorithms in topology optimization (2007, background): “A few approaches [16, 17, 19] have been proposed to remove such instability.”
On the trajectories of penalization methods for topology optimization (2001, background): “Another approach is to introduce local gradient constraints on the density variation (Petersson and Sigmund 1998; Zhou et al. 1999 ).”
A mass constraint formulation for structural topology optimization with multiphase materials (2011, methodology): “Besides, the design solution with the minimum length scale control [26, 27] is checkerboard-free.”