Research / Optimization

Topology optimization of an MBB beam

After Erik Andreassen, Anders Clausen, Mattias Schevenels, Boyan S. Lazarov, Ole Sigmund, “Efficient topology optimization in MATLAB using 88 lines of code”, Structural and Multidisciplinary Optimization (2010), doi:10.1007/s00158-010-0594-7.

Against the author’s code
12 of 12 checks pass· see the checks
Against the paper’s figures
Figure 3 settings reproduced; no digitized figure comparison or published compliance values claimed.

Research, not a design tool. Nothing here is an engineering result.

An educational SIMP optimizer: redistribute a fixed amount of material to reduce compliance.

The experiment

The authors’ abstract describes a compact successor to the 99-line code, adding density filtering and improving efficiency through preallocation and vectorization. Here we implement its main minimum-compliance method.

Each square uses a bilinear plane-stress element. SIMP interpolates its stiffness as E = 10⁻⁹ + ρᵖ(1 − 10⁻⁹). Optimality criteria redistribute material, with a move limit of 0.2. The engine’s sparse Cholesky solves equilibrium at every iteration.

Reproduction

Defaults: 60 × 20 elements, volume fraction 0.5, penalization 3, filter radius 2.4. These are section 3.4 and Figure 3(a) of the authors’ manuscript (pages 6–7). Sensitivity and density filtering use the same settings. Physical densities are shown.

Compliance is measured before each update; volume and density are recorded after it, exactly as in top88. Stop when the largest design change is at most 0.01. The reference overlay is shown only for matching default parameters.

Evidence and limitations

The reference runner downloads the authors’ unmodified function, checks its SHA-256, and observes full-precision data at its plotting calls in GNU Octave. Rust tests compare iteration counts, every compliance, volume and change, and final densities, alongside independent element and filter checks.

The accessible manuscript reports optimized images and timing tables, not final compliance or iteration counts for these cases. We do not claim a paper-figure comparison. Agreement between implementations is not experimental validation or engineering certification. Alternate boundary conditions are delegated to the 2001 paper; this experiment supports the MBB load case.

Abstract, manuscript and authors’ reference. Journal volume 43 (2011), pages 1–16; Crossref records the online publication in 2010.

Cite this

Stabileo Research, “Topology optimization of an MBB beam”, reproduction of Erik Andreassen, Anders Clausen, Mattias Schevenels, Boyan S. Lazarov, Ole Sigmund (2010), doi:10.1007/s00158-010-0594-7. Implementation: research/optimization/andreassen-2011 at commit 8068cd16ea2c. Engine: the Stabileo engine at the same commit. Permanent links to this exact build are planned.