Topology optimization using the unsmooth variational topology optimization (UNVARTOP) method: an educational implementat
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EDUCATIONAL PAPER
Topology optimization using the unsmooth variational topology optimization (UNVARTOP) method: an educational implementation in MATLAB Daniel Yago1,2 · Juan Cante1,2 · Oriol Lloberas-Valls2,3 · Javier Oliver2,3 Received: 30 March 2020 / Revised: 10 July 2020 / Accepted: 12 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper presents an efficient and comprehensive MATLAB code to solve two-dimensional structural topology optimization problems, including minimum mean compliance, compliant mechanism synthesis, and multi-load compliance problems. The unsmooth variational topology optimization (UNVARTOP) method, developed by Oliver et al. (Comput Methods Appl Mech Eng 355:779–819, 2019), is used in the topology optimization code, based on the finite element method (FEM), to compute the sensitivity and update the topology. The paper also includes instructions to improve the bisection algorithm, modify the computation of the Lagrangian multiplier by using an Augmented Lagrangian to impose the constraint, implement heat conduction problems, and extend the code to three-dimensional topology optimization problems. The code, intended for students and newcomers in topology optimization, is included as an appendix (Appendix A) and it can be downloaded from https://github.com/DanielYago/UNVARTOP together with supplementary material. Keywords Structural topology optimization · Relaxed topological derivative · Compliance · Compliant mechanism · Education · MATLAB code
1 Introduction The dissemination of the MATLAB code, included in this paper, is intended for education purposes, in order to provide students and those new to the field with the Responsible Editor: YoonYoung Kim Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00158-020-02722-0) contains supplementary material, which is available to authorized users. Javier Oliver
[email protected] 1
Escola Superior d’Enginyeries Industrial, Aeroespacial i Audiovisual de Terrassa (ESEIAAT), Technical University of Catalonia (UPC/Barcelona Tech), Campus Terrassa UPC, c/ Colom 11, 08222 Terrassa, Spain
2
Centre Internacional de M`etodes Num`erics en Enginyeria (CIMNE), Campus Nord UPC, M`odul C-1 101, c/ Jordi Girona 1-3, 08034 Barcelona, Spain
3
E.T.S d’Enginyers de Camins, Canals i Ports de Barcelona (ETSECCPB), Technical University of Catalonia (UPC/Barcelona Tech), Campus Nord UPC, M`odul C-1, c/ Jordi Girona 1-3, 08034 Barcelona, Spain
theoretical basis for topology optimization of structural problems as well as to familiarize a wider audience with the new technique. This article is inspired by similar ones (e.g., Sigmund 2001 and Andreassen et al. 2010) which presented a MATLAB implementation and possible extensions of other topology optimization approaches for structural problems. A wide variety of topology optimization approaches and the corresponding MATLAB implementations can be found in the literature, including the solid isotropic material with penalization
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