PolyTop3D: a three-dimensional Matlab implementation of topology ...
Blucher Material Science Proceedings Novembro de 2014, Número 1, Volume 1 www.proceedings.blucher.com.br/evento/mm-fgm2014
Oral Presentation
Poster Presentation
PolyTop3D: a three-dimensional Matlab implementation of topology optimization using unstructured polyhedral finite element meshes A. Pereira1, I.F.M. Menezes2, C. Talischi3, G.H. Paulino4 1
Pontifical Catholic University of Rio de Janeiro – PUC–Rio, [email protected] 2 Pontifical Catholic University of Rio de Janeiro – PUC–Rio, ivan@ puc-rio.br 3 University of Illinois at Urbana–Champaign – USA, [email protected] 4 University of Illinois at Urbana–Champaign – USA, [email protected]
Abstract The educational code PolyTop [1] was originally developed for topology optimization of two-dimensional elastic problems. This work presents an extension of PolyTop for three-dimensional problems using unstructured polyhedral finite element meshes. Similarly to the original PolyTop code, PolyTop3D 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. These features provide a framework on which other applications can be easily developed (e.g. compliant mechanisms, topology optimization for fluid flow, etc). We also demonstrate that other threedimensional codes using standard finite elements, such as bricks and tetrahedra, can be viewed as a special cases of PolyTop3D, which uses Wachspress elements [2]. The Matlab code is explained in detail and numerical examples are presented to illustrate its capabilities to solve three-dimensional problems.
Keywords: topology optimization, polytopes, Matlab, Voronoi diagrams, Wachspress
[1] Talischi, C., Paulino, G. H., Pereira, A., and Menezes, I. F. M., “PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes”, Struct Multidisc Optim, 45 (2012), 329–357. [2] Floater M., Gillette A. and Sukumar, N. “Gradient Bounds for Wachspress Coordinates on Polytopes”. Cornell University Library, Submitted on 18 Jun 2013. http://arxiv.org/abs/1306.4385.
Presenting author: DSc, A. Pereira, Brazil Corresponding author: DSc, A. Pereira, Brazil
Oral Presentation
Poster Presentation
PolyTop3D: a three-dimensional Matlab implementation of topology optimization using unstructured polyhedral finite element meshes A. Pereira1, I.F.M. Menezes2, C. Talischi3, G.H. Paulino4 1
Pontifical Catholic University of Rio de Janeiro – PUC–Rio, [email protected] 2 Pontifical Catholic University of Rio de Janeiro – PUC–Rio, ivan@ puc-rio.br 3 University of Illinois at Urbana–Champaign – USA, [email protected] 4 University of Illinois at Urbana–Champaign – USA, [email protected]
Abstract The educational code PolyTop [1] was originally developed for topology optimization of two-dimensional elastic problems. This work presents an extension of PolyTop for three-dimensional problems using unstructured polyhedral finite element meshes. Similarly to the original PolyTop code, PolyTop3D 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. These features provide a framework on which other applications can be easily developed (e.g. compliant mechanisms, topology optimization for fluid flow, etc). We also demonstrate that other threedimensional codes using standard finite elements, such as bricks and tetrahedra, can be viewed as a special cases of PolyTop3D, which uses Wachspress elements [2]. The Matlab code is explained in detail and numerical examples are presented to illustrate its capabilities to solve three-dimensional problems.
Keywords: topology optimization, polytopes, Matlab, Voronoi diagrams, Wachspress
[1] Talischi, C., Paulino, G. H., Pereira, A., and Menezes, I. F. M., “PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes”, Struct Multidisc Optim, 45 (2012), 329–357. [2] Floater M., Gillette A. and Sukumar, N. “Gradient Bounds for Wachspress Coordinates on Polytopes”. Cornell University Library, Submitted on 18 Jun 2013. http://arxiv.org/abs/1306.4385.
Presenting author: DSc, A. Pereira, Brazil Corresponding author: DSc, A. Pereira, Brazil
