Efficient topology optimization in MATLAB using 88 lines of code

By Erik Andreassen, Anders Clausen, Mattias Schevenels, Boyan S. Lazarov, Ole Sigmund. 2011

1,622 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/0262651dd8f03ead73b3ea00cc11d07c45e5867a

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Design of manufacturable 3D extremal elastic microstructure (2014, neutral): “A compact educational implementation of a typical topology optimization procedure can be found in (Andreassen et al., 2011).”
Multi-material topology optimization using ordered SIMP interpolation (2016, background): “If topology optimization problems are posed as dimensionless problems, λ usually can be a very large value, for example λ = 10(6) in the 99-line code (Sigmund 2001), λ=10(9) in the 88-line code (Andreassen et al. 2011), λ=10(9) in the top-3D code (Liu and Tovar 2014), λ=10(9) in the active-phase alg”
Improving the efficiency of large scale topology optimization through on‐the‐fly reduced order model construction (2015, methodology): “[25] for the 2D topology optimization problem and from Liu and Tovar [26] for the 3D problem.”
Topology design with negative masks using gradient search (2011, methodology): “The code is inspired by the previous educational articles on topology optimization that employ SIMP and level set methods (e.g., Sigmund 2001; Challis 2010; Andreassen et al. 2011).”
An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions (2018, methodology): “The assembly of the global stiffness matrix K also follows almost the same procedure as in the 88-line code (Andreassen et al. 2011) with the index vectors iK and jK and the element-wise matrix sK .”
Deep Generative Design: Integration of Topology Optimization and Generative Models (2019, methodology): “The element stiffness matrix is based on four-node bilinear square elements in the 88-line MATLAB code [32].”
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).”
Large scale three-dimensional topology optimisation of heat sinks cooled by natural convection (2015, background): “Keywords: topology optimisation, heat sink design, natural convection, large scale, multiphysics optimisation”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “Related to the second method, Andreassen et al. (2011) specify several simple concepts for computational efficiency in MATLAB implementations of topology optimization.”
Bi-directional Evolutionary Structural Optimization on Advanced Structures and Materials: A Comprehensive Review (2016, methodology): “Both codes are built on top of the 88-line code [3] with the implementation of the hard-kill BESO method.”
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).”
Deep learning for determining a near-optimal topological design without any iteration (2018, methodology): “First, datasets of the optimized structures paired with the information on optimization settings and boundary conditions were generated using the open-source topology optimization code (Andreassen et al. 2011).”