Details
| Original language | English |
|---|---|
| Pages (from-to) | 780-801 |
| Number of pages | 22 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 310 |
| Publication status | Published - 1 Oct 2016 |
| Externally published | Yes |
Abstract
Previous works of Junker and Hackl (2016) have presented a variational growth approach to topology optimization in which the problem of checkerboarding was suppressed by means of a discontinuous regularization scheme. This approach did not require additional filter techniques and also optimization algorithms were not needed any more. However, growth approaches to topology optimization demand some limitations in order to avoid a global and simultaneous generation of mass. The limitation has been achieved by a rather simple approach with restricted possibilities for controlling. In this contribution, we eliminate this drawback by introducing a Lagrange multiplier to control the total mass within the model space for each iteration step. This enables us to achieve directly controlled growth behavior and even find optimized structures for prescribed structure volumes. Furthermore, a modified growth approach, which we refer to as the Lagrange shift approach, results a numerically stable model that is easy to handle. After the derivation of the approach, we present numerical solutions for different boundary problems that demonstrate the potential of our model.
Keywords
- Constraint evolution, Discontinuous Galerkin approach, Growth, Topology optimization, Variational modeling
ASJC Scopus subject areas
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
- Engineering(all)
- Computational Mechanics
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 310, 01.10.2016, p. 780-801.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An evolutionary topology optimization approach with variationally controlled growth
AU - Jantos, D.R.
AU - Junker, P.
AU - Hackl, K.
N1 - Publisher Copyright: © 2016 Elsevier B.V.
PY - 2016/10/1
Y1 - 2016/10/1
N2 - Previous works of Junker and Hackl (2016) have presented a variational growth approach to topology optimization in which the problem of checkerboarding was suppressed by means of a discontinuous regularization scheme. This approach did not require additional filter techniques and also optimization algorithms were not needed any more. However, growth approaches to topology optimization demand some limitations in order to avoid a global and simultaneous generation of mass. The limitation has been achieved by a rather simple approach with restricted possibilities for controlling. In this contribution, we eliminate this drawback by introducing a Lagrange multiplier to control the total mass within the model space for each iteration step. This enables us to achieve directly controlled growth behavior and even find optimized structures for prescribed structure volumes. Furthermore, a modified growth approach, which we refer to as the Lagrange shift approach, results a numerically stable model that is easy to handle. After the derivation of the approach, we present numerical solutions for different boundary problems that demonstrate the potential of our model.
AB - Previous works of Junker and Hackl (2016) have presented a variational growth approach to topology optimization in which the problem of checkerboarding was suppressed by means of a discontinuous regularization scheme. This approach did not require additional filter techniques and also optimization algorithms were not needed any more. However, growth approaches to topology optimization demand some limitations in order to avoid a global and simultaneous generation of mass. The limitation has been achieved by a rather simple approach with restricted possibilities for controlling. In this contribution, we eliminate this drawback by introducing a Lagrange multiplier to control the total mass within the model space for each iteration step. This enables us to achieve directly controlled growth behavior and even find optimized structures for prescribed structure volumes. Furthermore, a modified growth approach, which we refer to as the Lagrange shift approach, results a numerically stable model that is easy to handle. After the derivation of the approach, we present numerical solutions for different boundary problems that demonstrate the potential of our model.
KW - Constraint evolution
KW - Discontinuous Galerkin approach
KW - Growth
KW - Topology optimization
KW - Variational modeling
UR - http://www.scopus.com/inward/record.url?scp=84982227866&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2016.07.022
DO - 10.1016/j.cma.2016.07.022
M3 - Article
VL - 310
SP - 780
EP - 801
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
ER -