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 35 articles , 1 standard article )

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  1. 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)
  2. Natarajan, Sundararajan: On the application of polygonal finite element method for Stokes flow -- a comparison between equal order and different order approximation (2020)
  3. 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)
  4. Ho-Nguyen-Tan, Thuan; Kim, Hyun-Gyu: Polygonal shell elements with assumed transverse shear and membrane strains (2019)
  5. Lagaros, Nikos D.; Vasileiou, Nikos; Kazakis, Georgios: A C# code for solving 3D topology optimization problems using SAP2000 (2019)
  6. Nguyen-Xuan, H.; Chau, Khanh N.; Chau, Khai N.: Polytopal composite finite elements (2019)
  7. Wang, Hui; Qin, Qing-Hua; Lee, Cheuk-Yu: (n)-sided polygonal hybrid finite elements with unified fundamental solution kernels for topology optimization (2019)
  8. 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)
  9. Gravenkamp, Hauke; Natarajan, Sundararajan: Scaled boundary polygons for linear elastodynamics (2018)
  10. Jensen, Kristian Ejlebjerg: Topology optimization of Stokes flow on dynamic meshes using simple optimizers (2018)
  11. Nguyen-Xuan, H.; Do, Hien V.; Chau, Khanh N.: An adaptive strategy based on conforming quadtree meshes for kinematic limit analysis (2018)
  12. Perumal, Logah: A brief review on polygonal/polyhedral finite element methods (2018)
  13. Sanders, Emily D.; Aguiló, Miguel A.; Paulino, Glaucio H.: Multi-material continuum topology optimization with arbitrary volume and mass constraints (2018)
  14. Vaziri Astaneh, Ali; Fuentes, Federico; Mora, Jaime; Demkowicz, Leszek: High-order polygonal discontinuous Petrov-Galerkin (PolyDPG) methods using ultraweak formulations (2018)
  15. Antonietti, Paola F.; Bruggi, Matteo; Scacchi, Simone; Verani, Marco: On the virtual element method for topology optimization on polygonal meshes: a numerical study (2017)
  16. Chi, H.; da Veiga, L. Beirão; Paulino, G. H.: Some basic formulations of the virtual element method (VEM) for finite deformations (2017)
  17. Nguyen-Xuan, H.; Nguyen-Hoang, Son; Rabczuk, T.; Hackl, K.: A polytree-based adaptive approach to limit analysis of cracked structures (2017)
  18. Zhang, Xiaojia Shelly; de Sturler, Eric; Paulino, Glaucio H.: Stochastic sampling for deterministic structural topology optimization with many load cases: density-based and ground structure approaches (2017)
  19. Duczek, Sascha; Gabbert, Ulrich: The finite cell method for polygonal meshes: poly-FCM (2016)
  20. Beirão da Veiga, Lourenço; Manzini, Gianmarco; Putti, Mario: Post processing of solution and flux for the nodal mimetic finite difference method (2015)

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