Topology optimization with anisotropic materials, including a filter to smooth fiber pathways

authored by: Dustin Roman Jantos, Klaus Hackl, Philipp Junker
Abstract: In a recent publication, an approach to optimize the orientation of anisotropic materials was presented. This strategy was embedded into the thermodynamic topology optimization based on growth. In this paper, we show that the thermodynamic orientation optimization can also be used in more classical approaches to topology optimization. We furthermore enhance the approach by a novel filtering technique to provide control over the smoothness of the pathway of principal material directions, i.e., the curvature of fibers. The filter is based on a convolution operator and is applied to the material stiffness tensor, so that the filtering technique is not directly bounded to the actual parameterization for the design variables. To this end, the topology is defined by a continuous density approach with penalization of intermediate densities (SIMP) solved via the optimality criteria method (OCM). A set of three continuous Euler angles is used as additional design variables to describe the local material rotation of the anisotropic base material. The thermodynamic optimization of the material orientation is performed by evolution of the Euler angles to minimize the elastic energy. The related evolution equations are derived by means of the Hamilton principle, well-known from material modeling.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Ruhr-Universität Bochum
Type: Article
Journal: Structural and Multidisciplinary Optimization
Volume: 61
Pages: 2135-2154
No. of pages: 20
ISSN: 1615-147X
Publication date: 05.2020
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Software, Control and Systems Engineering, Computer Science Applications, Computer Graphics and Computer-Aided Design, Control and Optimization
Electronic version(s): https://doi.org/10.1007/s00158-019-02461-x (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{3ba816f7114a49eeb8c7a1b90abbea36,
title = "Topology optimization with anisotropic materials, including a filter to smooth fiber pathways",
abstract = "In a recent publication, an approach to optimize the orientation of anisotropic materials was presented. This strategy was embedded into the thermodynamic topology optimization based on growth. In this paper, we show that the thermodynamic orientation optimization can also be used in more classical approaches to topology optimization. We furthermore enhance the approach by a novel filtering technique to provide control over the smoothness of the pathway of principal material directions, i.e., the curvature of fibers. The filter is based on a convolution operator and is applied to the material stiffness tensor, so that the filtering technique is not directly bounded to the actual parameterization for the design variables. To this end, the topology is defined by a continuous density approach with penalization of intermediate densities (SIMP) solved via the optimality criteria method (OCM). A set of three continuous Euler angles is used as additional design variables to describe the local material rotation of the anisotropic base material. The thermodynamic optimization of the material orientation is performed by evolution of the Euler angles to minimize the elastic energy. The related evolution equations are derived by means of the Hamilton principle, well-known from material modeling.",
keywords = "Anisotropic material, Continous fiber angle optimization, Material orientation filter, Thermodynamic optimization, Topology optimization",
author = "Jantos, {Dustin Roman} and Klaus Hackl and Philipp Junker",
year = "2020",
month = may,
doi = "10.1007/s00158-019-02461-x",
language = "English",
volume = "61",
pages = "2135--2154",
journal = "Structural and Multidisciplinary Optimization",
issn = "1615-147X",
publisher = "Springer Verlag",
number = "5",
}