A 99 line topology optimization code written in Matlab

By Ole Sigmund. 2001

2,783 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/e9331af59ba3ac3781ca5f036aefba7274a6e9ed

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Deep Generative Design: Integration of Topology Optimization and Generative Models (2019, methodology): “The basic formulation of SIMP in compliance minimization can be written as [29,30]”
Non-probabilistic reliability-based topology optimization with multidimensional parallelepiped convex model (2017, background): “Since the work of Bendsøe and Kikuchi (1988), topology optimization methods for continuum structures based on the material distribution model have experienced great popularity, such as solid isotropic material with penalization (SIMP) and its variants (Bendsøe and Sigmund 1999; Sigmund 2001), evolut”
Structural topology optimization for multiple load cases using a dynamic aggregation technique (2009, background): “While this problem can be eliminated with filtering techniques, these tend to produce fuzzy boundaries comprising regions of intermediate-density (Sigmund and Petersson 1998 , Sigmund 2001 ).”
Stress-constrained topology optimization: a topological level-set approach (2013, methodology): “These density variables define the topology as described, for example in Sigmund (2001).”
On filter boundary conditions in topology optimization (2017, methodology): “The most simple approaches only involve a single, basic filter (Sigmund, 2001; Andreassen et al, 2011), such as the sensitivity filter (Sigmund, 1994, 1997) or the density filter (Bruns and Tortorelli, 2001; Bourdin, 2001), potentially in the form of a PDE-based filter (Lazarov and Sigmund, 2011).”
PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab (2012, methodology): “For instance, in addition to the popular “99 line” code (Sigmund 2001) and its successor (Andreassen et al. 2011), Allaire and Pantz (2006) presented a structural optimization code based on FreeFem++. Liu et al. (2005) introduced a coupled level set method using the FEMLAB package and Challis…”
Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models (2009, positive): “However, for better suppressing the checkerboard patterns and the mesh-dependency, the well-known sensitivity filter technique [54] is also employed in this study.”
Efficient topology optimization in MATLAB using 88 lines of code (2011, methodology): “An example is Sigmund’s 99 line topology optimization code (Sigmund, 2001).”
An efficient 3D topology optimization code written in Matlab (2014, neutral): “For M ATLAB , Sigmund (2001) introduced the 99-line program for two-dimensional topology optimization.”
Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics (2001, background): “…Chen and Kikuchi (2000), software development: Thomas and Schramm (2000), general review: Sigmund (2000c), education: Sigmund (2001a), Tcherniak and Sigmund (2001) convergence studies: Stolpe and Svanberg (2001), combined optimization of material and structure: Rodrigues, Guedes and Bendsøe…”
Filters in topology optimization based on Helmholtz‐type differential equations (2011, methodology): “The optimization can be achieved by several different iterative procedures [17, 18].”
An additive manufacturing filter for topology optimization of print-ready designs (2016, methodology): “For the full problem definition the reader is referred to Sigmund (2001) and Andreassen et al. (2011).”