An accurate and fast regularization approach to thermodynamic topology optimization

verfasst von
Dustin Roman Jantos, Klaus Hackl, Philipp Junker
Abstract

In a series of previous works, we established a novel approach to topology optimization for compliance minimization based on thermodynamic principles known from the field of material modeling. Hamilton's principle for dissipative processes directly yields a partial differential equation (referred to as the evolution equation) as an update scheme for the spatial distribution of density mass describing the topology. Consequently, no additional mathematical minimization algorithms are needed. In this article, we introduce a regularization scheme by penalization of the gradient of the spatial distribution of mass density. The parabolic evolution equation (owing to a similar structure to the transient heat-conduction equation) is solved most efficiently by an explicit time discretization. The Laplace operator is discretized via a Taylor series expansion yielding an operator matrix that is constant for the entire optimization process. This method shares some similarities to meshless methods and allows for an accurate application also on unstructured finite element meshes. The minimal size of the structure member can directly be controlled, a priori, by a numerical parameter introduced along with the regularization, similar to classical filter radii.

Organisationseinheit(en)
Institut für Kontinuumsmechanik
Externe Organisation(en)
Ruhr-Universität Bochum
Typ
Artikel
Journal
International Journal for Numerical Methods in Engineering
Band
117
Seiten
991-1017
Anzahl der Seiten
27
ISSN
0029-5981
Publikationsdatum
02.03.2019
Publikationsstatus
Veröffentlicht
Peer-reviewed
Ja
ASJC Scopus Sachgebiete
Numerische Mathematik, Ingenieurwesen (insg.), Angewandte Mathematik
Elektronische Version(en)
https://doi.org/10.1002/nme.5988 (Zugang: Geschlossen)
 

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