PolyTop

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 15 articles , 1 standard article )

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  1. Duczek, Sascha; Gabbert, Ulrich: The finite cell method for polygonal meshes: poly-FCM (2016)
  2. Beirão da Veiga, Lourenço; Manzini, Gianmarco; Putti, Mario: Post processing of solution and flux for the nodal mimetic finite difference method (2015)
  3. Chi, Heng; Talischi, Cameron; Lopez-Pamies, Oscar; H.Paulino, Glaucio: Polygonal finite elements for finite elasticity (2015)
  4. Duczek, Sascha; Gabbert, Ulrich: Efficient integration method for fictitious domain approaches (2015)
  5. Natarajan, Sundararajan; Bordas, Stéphane Pa; Ooi, Ean Tat: Virtual and smoothed finite elements: a connection and its application to polygonal/polyhedral finite element methods (2015)
  6. Talischi, Cameron: A family of $H(\mathrmdiv)$ finite element approximations on polygonal meshes (2015)
  7. Talischi, Cameron; Pereira, Anderson; Menezes, Ivan F.M.; Paulino, Glaucio H.: Gradient correction for polygonal and polyhedral finite elements (2015)
  8. Chiong, Irene; Ooi, Ean Tat; Song, Chongmin; Tin-Loi, Francis: Scaled boundary polygons with application to fracture analysis of functionally graded materials (2014)
  9. Leon, S.E.; Spring, D.W.; Paulino, G.H.: Reduction in mesh bias for dynamic fracture using adaptive splitting of polygonal finite elements (2014)
  10. Sukumar, N.: Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons (2013)
  11. Suresh, Krishnan: Efficient generation of large-scale Pareto-optimal topologies (2013)
  12. Talischi, Cameron; Paulino, Glaucio H.: An operator splitting algorithm for Tikhonov-regularized topology optimization (2013)
  13. Vatanabe, S.L.; Paulino, G.H.; Silva, E.C.N.: Design of functionally graded piezocomposites using topology optimization and homogenization -- toward effective energy harvesting materials (2013)
  14. Talischi, Cameron; Paulino, Glaucio H.; Pereira Anderson; Menezes, Ivan F.M.: PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes (2012)
  15. Talischi, Cameron; Paulino, Glaucio H.; Pereira Anderson; Menezes, Ivan F.M.: PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab (2012)