Optimized growth and reorientation of anisotropic material based on evolution equations

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Original languageEnglish
Pages (from-to)47-66
Number of pages20
JournalComputational mechanics
Volume62
Issue number1
Early online date18 Sept 2017
Publication statusPublished - Jul 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

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Cite this

Optimized growth and reorientation of anisotropic material based on evolution equations. / Jantos, Dustin R.; Hackl, Klaus; Junker, Philipp.
In: Computational mechanics, Vol. 62, No. 1, 07.2018, p. 47-66.

Research output: Contribution to journalArticleResearchpeer review

Jantos DR, Hackl K, Junker P. Optimized growth and reorientation of anisotropic material based on evolution equations. Computational mechanics. 2018 Jul;62(1):47-66. Epub 2017 Sept 18. doi: 10.1007/s00466-017-1483-3
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