PolyTop3D: a three-dimensional Matlab implementation of topology optimization using unstructured polyhedral finite element meshes

PolyTop3D: a three-dimensional Matlab implementation of topology optimization using unstructured polyhedral finite element meshes

Pereira, A.; Menezes, I.F.M.; Talischi, C.; Paulino, G.H.

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.

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.

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Como citar:

Pereira, A.; Menezes, I.F.M.; Talischi, C.; Paulino, G.H.; "PolyTop3D: a three-dimensional Matlab implementation of topology optimization using unstructured polyhedral finite element meshes", p-87-87. In: Proceedings of the 13th International Symposium on Multiscale, Multifunctional and Functionally Graded Materials [=Blucher Material Science Proceedings, v.1, n.1]. São Paulo: Blucher, 2014.
ISSN 23589337, DOI