PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes. We present an efficient Matlab code for structural topology optimization that includes a general finite element routine based on isoparametric polygonal elements which can be viewed as the extension of linear triangles and bilinear quads. The code also features a modular structure in which the analysis routine and the optimization algorithm are separated from the specific choice of topology optimization formulation. Within this framework, the finite element and sensitivity analysis routines contain no information related to the formulation and thus can be extended, developed and modified independently. We address issues pertaining to the use of unstructured meshes and arbitrary design domains in topology optimization that have received little attention in the literature. Also, as part of our examination of the topology optimization problem, we review the various steps taken in casting the optimal shape problem as a sizing optimization problem. This endeavor allows us to isolate the finite element and geometric analysis parameters and how they are related to the design variables of the discrete optimization problem. The Matlab code is explained in detail and numerical examples are presented to illustrate the capabilities of the code.

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 45 articles , 1 standard article )

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  1. Adak, D.; Manzini, G.; Natarajan, S.: Virtual element approximation of two-dimensional parabolic variational inequalities (2022)
  2. Nguyen, Nam V.; Nguyen-Xuan, H.; Lee, Jaehong: Polygonal composite elements for stress-constrained topology optimization of nearly incompressible materials (2022)
  3. Sreekumar, Abhilash; Triantafyllou, Savvas P.; Chevillotte, Fabien: Virtual elements for sound propagation in complex poroelastic media (2022)
  4. Chi, Heng; Zhang, Yuyu; Tang, Tsz Ling Elaine; Mirabella, Lucia; Dalloro, Livio; Song, Le; Paulino, Glaucio H.: Universal machine learning for topology optimization (2021)
  5. Liu, Yang; Yang, Cheng; Wei, Peng; Zhou, Pingzhang; Du, Jianbin: An ODE-driven level-set density method for topology optimization (2021)
  6. Sreekumar, Abhilash; Triantafyllou, Savvas P.; Bécot, François-Xavier; Chevillotte, Fabien: Multiscale VEM for the Biot consolidation analysis of complex and highly heterogeneous domains (2021)
  7. Adak, Dibyendu; Pramod, ALN; Ooi, Ean Tat; Natarajan, Sundararajan: A combined virtual element method and the scaled boundary finite element method for linear elastic fracture mechanics (2020)
  8. Alberto Paganini, Florian Wechsung: Fireshape: a shape optimization toolbox for Firedrake (2020) arXiv
  9. da Costa, R. O. S. S.; Pinho, S. T.: A novel formulation for the explicit discretisation of evolving boundaries with application to topology optimisation (2020)
  10. Fernández, Eduardo; Yang, Kai-ke; Koppen, Stijn; Alarcón, Pablo; Bauduin, Simon; Duysinx, Pierre: Imposing minimum and maximum member size, minimum cavity size, and minimum separation distance between solid members in topology optimization (2020)
  11. Natarajan, Sundararajan: On the application of polygonal finite element method for Stokes flow -- a comparison between equal order and different order approximation (2020)
  12. Zhang, Xiaojia Shelly; Chi, Heng; Paulino, Glaucio H.: Adaptive multi-material topology optimization with hyperelastic materials under large deformations: a virtual element approach (2020)
  13. Zobaer, S. M. Tareq; Sutradhar, Alok: An energy-based method for interface connectivity of incompatible microstructures through parametric modeling (2020)
  14. Chi, Heng; Beirão da Veiga, Lourenço; Paulino, Glaucio H.: A simple and effective gradient recovery scheme and \textitaposteriori error estimator for the virtual element method (VEM) (2019)
  15. Ho-Nguyen-Tan, Thuan; Kim, Hyun-Gyu: Polygonal shell elements with assumed transverse shear and membrane strains (2019)
  16. Lagaros, Nikos D.; Vasileiou, Nikos; Kazakis, Georgios: A C# code for solving 3D topology optimization problems using SAP2000 (2019)
  17. Nguyen-Xuan, H.; Chau, Khanh N.; Chau, Khai N.: Polytopal composite finite elements (2019)
  18. Wang, Hui; Qin, Qing-Hua; Lee, Cheuk-Yu: (n)-sided polygonal hybrid finite elements with unified fundamental solution kernels for topology optimization (2019)
  19. Chau, Khai N.; Chau, Khanh N.; Ngo, Tuan; Hackl, Klaus; Nguyen-Xuan, H.: A polytree-based adaptive polygonal finite element method for multi-material topology optimization (2018)
  20. Gravenkamp, Hauke; Natarajan, Sundararajan: Scaled boundary polygons for linear elastodynamics (2018)

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