A discontinuous phase field approach to variational growth-based topology optimization

authored by: Philipp Junker, Klaus Hackl
Abstract: Numerical instabilities cause the well-known problem of checkerboarding during topology optimization: elements that possess material are periodically neighbored to elements that are material-free. Furthermore, such numerical solutions depend on the finite element mesh and no reasonable processing techniques exist for manufacture. Thus, integral- or gradient-based regularization techniques are usually applied during topology optimization. In this paper, a novel approach to regularization is derived for a recently published variational approach to topology optimization that is based on material growth. The presented approach shares some similarities with the discontinuous Galerkin method and completely removes consideration of additional nodal quantities or complex integration schemes. The derivation and numerical treatment of the resulting phase field equation as well as exemplary numerical results are presented.
External Organisation(s): The University of Wuppertal
Type: Article
Journal: Structural and Multidisciplinary Optimization
Volume: 54
Pages: 81-94
No. of pages: 14
ISSN: 1615-147X
Publication date: 01.07.2016
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Software, Control and Systems Engineering, Computer Science Applications, Control and Optimization, Computer Graphics and Computer-Aided Design
Electronic version(s): https://doi.org/10.1007/s00158-016-1398-1 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{0c70d75ec7874aaeabe9d53407dbde24,
title = "A discontinuous phase field approach to variational growth-based topology optimization",
abstract = "Numerical instabilities cause the well-known problem of checkerboarding during topology optimization: elements that possess material are periodically neighbored to elements that are material-free. Furthermore, such numerical solutions depend on the finite element mesh and no reasonable processing techniques exist for manufacture. Thus, integral- or gradient-based regularization techniques are usually applied during topology optimization. In this paper, a novel approach to regularization is derived for a recently published variational approach to topology optimization that is based on material growth. The presented approach shares some similarities with the discontinuous Galerkin method and completely removes consideration of additional nodal quantities or complex integration schemes. The derivation and numerical treatment of the resulting phase field equation as well as exemplary numerical results are presented.",
keywords = "Discontinuous phase field, Growth-based topology optimization, Regularization, Variational modeling",
author = "Philipp Junker and Klaus Hackl",
note = "Publisher Copyright: {\textcopyright} 2016, Springer-Verlag Berlin Heidelberg.",
year = "2016",
month = jul,
day = "1",
doi = "10.1007/s00158-016-1398-1",
language = "English",
volume = "54",
pages = "81--94",
journal = "Structural and Multidisciplinary Optimization",
issn = "1615-147X",
publisher = "Springer Verlag",
number = "1",
}