Optimized growth and reorientation of anisotropic material based on evolution equations

authored by
D.R. Jantos, P. Junker, K. Hackl
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.

Organisation(s)
Institute of Continuum Mechanics
Type
Article
Journal
Computational mechanics
Volume
62
Pages
47-66
No. of pages
20
ISSN
0178-7675
Publication date
2018
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s)
https://doi.org/10.1007/s00466-017-1483-3 (Access: Closed)
 

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