Details
| Original language | English |
|---|---|
| Pages (from-to) | 47-66 |
| Number of pages | 20 |
| Journal | Computational mechanics |
| Volume | 62 |
| Issue number | 1 |
| Publication status | Published - 2018 |
Abstract
Modern high-performance materials have inherent anisotropic elastic properties. The local material orientation can thus be considered to be an additional design variable for the topology optimization of structures containing such materials. In our previous work, we introduced a variational growth approach to topology optimization for isotropic, linear-elastic materials. We solved the optimization problem purely by application of Hamilton’s principle. In this way, we were able to determine an evolution equation for the spatial distribution of density mass, which can be evaluated in an iterative process within a solitary finite element environment. We now add the local material orientation described by a set of three Euler angles as additional design variables into the three-dimensional model. This leads to three additional evolution equations that can be separately evaluated for each (material) point. Thus, no additional field unknown within the finite element approach is needed, and the evolution of the spatial distribution of density mass and the evolution of the Euler angles can be evaluated simultaneously.
Keywords
- Anisotropic, Energy methods, Internal variable, Optimization
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational mechanics, Vol. 62, No. 1, 2018, p. 47-66.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Optimized growth and reorientation of anisotropic material based on evolution equations
AU - Jantos, D.R.
AU - Junker, P.
AU - Hackl, K.
N1 - Publisher Copyright: © 2017, Springer-Verlag GmbH Germany.
PY - 2018
Y1 - 2018
N2 - Modern high-performance materials have inherent anisotropic elastic properties. The local material orientation can thus be considered to be an additional design variable for the topology optimization of structures containing such materials. In our previous work, we introduced a variational growth approach to topology optimization for isotropic, linear-elastic materials. We solved the optimization problem purely by application of Hamilton’s principle. In this way, we were able to determine an evolution equation for the spatial distribution of density mass, which can be evaluated in an iterative process within a solitary finite element environment. We now add the local material orientation described by a set of three Euler angles as additional design variables into the three-dimensional model. This leads to three additional evolution equations that can be separately evaluated for each (material) point. Thus, no additional field unknown within the finite element approach is needed, and the evolution of the spatial distribution of density mass and the evolution of the Euler angles can be evaluated simultaneously.
AB - Modern high-performance materials have inherent anisotropic elastic properties. The local material orientation can thus be considered to be an additional design variable for the topology optimization of structures containing such materials. In our previous work, we introduced a variational growth approach to topology optimization for isotropic, linear-elastic materials. We solved the optimization problem purely by application of Hamilton’s principle. In this way, we were able to determine an evolution equation for the spatial distribution of density mass, which can be evaluated in an iterative process within a solitary finite element environment. We now add the local material orientation described by a set of three Euler angles as additional design variables into the three-dimensional model. This leads to three additional evolution equations that can be separately evaluated for each (material) point. Thus, no additional field unknown within the finite element approach is needed, and the evolution of the spatial distribution of density mass and the evolution of the Euler angles can be evaluated simultaneously.
KW - Anisotropic
KW - Energy methods
KW - Internal variable
KW - Optimization
UR - http://www.scopus.com/inward/record.url?scp=85029601346&partnerID=8YFLogxK
U2 - 10.1007/s00466-017-1483-3
DO - 10.1007/s00466-017-1483-3
M3 - Article
VL - 62
SP - 47
EP - 66
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 1
ER -