Lennart Scherz, Benedikt Kriegesmann, Claus B. W. Pedersen
{"title":"A condition number-based numerical stabilization method for geometrically nonlinear topology optimization","authors":"Lennart Scherz, Benedikt Kriegesmann, Claus B. W. Pedersen","doi":"10.1002/nme.7574","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"125 23","pages":""},"PeriodicalIF":2.7000,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7574","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal for Numerical Methods in Engineering","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/nme.7574","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍:
The International Journal for Numerical Methods in Engineering publishes original papers describing significant, novel developments in numerical methods that are applicable to engineering problems.
The Journal is known for welcoming contributions in a wide range of areas in computational engineering, including computational issues in model reduction, uncertainty quantification, verification and validation, inverse analysis and stochastic methods, optimisation, element technology, solution techniques and parallel computing, damage and fracture, mechanics at micro and nano-scales, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, and error estimation and mesh generation. It is emphasized that this is by no means an exhaustive list, and particularly papers on multi-scale, multi-physics or multi-disciplinary problems, and on new, emerging topics are welcome.