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A condition number-based numerical stabilization method for geometrically nonlinear topology optimization
Citation Link: https://doi.org/10.15480/882.13755
Publikationstyp
Journal Article
Date Issued
2024-12-15
Sprache
English
Author(s)
Dassault Systemes Deutschland GmbH
TORE-DOI
Volume
125
Issue
23
Article Number
e7574
Citation
International Journal for Numerical Methods in Engineering 125 (23): e7574 (2024)
Publisher DOI
Scopus ID
Publisher
Wiley
The current paper introduces a new stabilization scheme for void and low-density elements for geometrical nonlinear topology optimization. Frequently, certain localized regions in the geometrical nonlinear finite element analysis of the topology optimization have excessive artificial distortions due to the low stiffness of the void and low-density elements. The present stabilization applies a hyperelastic constitutive material model for the numerical stabilization that is associated with the condition number of the deformation gradient and thereby, is associated with the numerical conditioning of the mapping between current configuration and reference configuration of the underlying continuum mechanics on a constitutive material model level. The stabilization method is independent upon the topology design variables during the optimization iterations. Numerical parametric studies show that the parameters for the constitutive hyperelasticity material of the new stabilization scheme are governed by the stiffness of the constitutive model of the initial physical system. The parametric studies also show that the stabilization scheme is independently upon the type of constitutive model of the physical system and the element types applied for the finite element modeling. The new stabilization scheme is numerical verified using both academic reference examples and industrial applications. The numerical examples show that the number of optimization iterations is significantly reduced compared to the stabilization approaches previously reported in the literature.
Subjects
condition number | geometrically nonlinear modeling | hyperelastic material model | numerical stabilization | static analysis | topology optimization | transient analysis
DDC Class
620.1: Engineering Mechanics and Materials Science
Publication version
publishedVersion
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Name
Numerical Meth Engineering - 2024 - Scherz - A condition number‐based numerical stabilization method for geometrically.pdf
Type
Main Article
Size
16.32 MB
Format
Adobe PDF