Details
| Original language | English |
|---|---|
| Pages (from-to) | 991-1017 |
| Number of pages | 27 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 117 |
| Issue number | 9 |
| Publication status | Published - 2 Mar 2019 |
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.
Keywords
- meshless Laplacian, parabolic PDE, regularization, thermodynamic topology optimization, unstructured meshes, variational material modeling
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Engineering(all)
- General Engineering
- Mathematics(all)
- Applied Mathematics
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In: International Journal for Numerical Methods in Engineering, Vol. 117, No. 9, 02.03.2019, p. 991-1017.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An accurate and fast regularization approach to thermodynamic topology optimization
AU - Jantos, Dustin Roman
AU - Hackl, Klaus
AU - Junker, Philipp
N1 - Publisher Copyright: © 2018 John Wiley & Sons, Ltd.
PY - 2019/3/2
Y1 - 2019/3/2
N2 - 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.
AB - 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.
KW - meshless Laplacian
KW - parabolic PDE
KW - regularization
KW - thermodynamic topology optimization
KW - unstructured meshes
KW - variational material modeling
UR - http://www.scopus.com/inward/record.url?scp=85057721692&partnerID=8YFLogxK
U2 - 10.1002/nme.5988
DO - 10.1002/nme.5988
M3 - Article
VL - 117
SP - 991
EP - 1017
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 9
ER -