A new variational approach for the thermodynamic topology optimization of hyperelastic structures

authored by: Philipp Junker, Daniel Balzani
Abstract: We present a novel approach to topology optimization based on thermodynamic extremal principles. This approach comprises three advantages: (1) it is valid for arbitrary hyperelastic material formulations while avoiding artificial procedures that were necessary in our previous approaches for topology optimization based on thermodynamic principles; (2) the important constraints of bounded relative density and total structure volume are fulfilled analytically which simplifies the numerical implementation significantly; (3) it possesses a mathematical structure that allows for a variety of numerical procedures to solve the problem of topology optimization without distinct optimization routines. We present a detailed model derivation including the chosen numerical discretization and show the validity of the approach by simulating two boundary value problems with large deformations.
External Organisation(s): Ruhr-Universität Bochum
Type: Article
Journal: Computational mechanics
Volume: 67
Pages: 455-480
No. of pages: 26
ISSN: 0178-7675
Publication date: 02.2021
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/s00466-020-01949-4 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{1e4e2d784e154cd986fc047827f2e005,
title = "A new variational approach for the thermodynamic topology optimization of hyperelastic structures",
abstract = "We present a novel approach to topology optimization based on thermodynamic extremal principles. This approach comprises three advantages: (1) it is valid for arbitrary hyperelastic material formulations while avoiding artificial procedures that were necessary in our previous approaches for topology optimization based on thermodynamic principles; (2) the important constraints of bounded relative density and total structure volume are fulfilled analytically which simplifies the numerical implementation significantly; (3) it possesses a mathematical structure that allows for a variety of numerical procedures to solve the problem of topology optimization without distinct optimization routines. We present a detailed model derivation including the chosen numerical discretization and show the validity of the approach by simulating two boundary value problems with large deformations.",
keywords = "Large deformation, Topology optimization, Variational method",
author = "Philipp Junker and Daniel Balzani",
year = "2021",
month = feb,
doi = "10.1007/s00466-020-01949-4",
language = "English",
volume = "67",
pages = "455--480",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "2",
}