An interface-enriched generalized finite element method for level set-based topology optimization
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RESEARCH PAPER
An interface-enriched generalized finite element method for level set-based topology optimization S. J. van den Boom1
· J. Zhang1
· F. van Keulen1
´ 1 · A. M. Aragon
Received: 15 February 2020 / Revised: 11 June 2020 / Accepted: 7 July 2020 © The Author(s) 2020
Abstract During design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A level set description of the boundary, when combined with an enriched finite element formulation, offers a smoother description of the design than traditional density-based methods. However, existing enriched methods have drawbacks, including ill-conditioning and difficulties in prescribing essential boundary conditions. In this work, we introduce a new enriched topology optimization methodology that overcomes the aforementioned drawbacks; boundaries are resolved accurately by means of the Interface-enriched Generalized Finite Element Method (IGFEM), coupled to a level set function constructed by radial basis functions. The enriched method used in this new approach to topology optimization has the same level of accuracy in the analysis as the standard finite element method with matching meshes, but without the need for remeshing. We derive the analytical sensitivities and we discuss the behavior of the optimization process in detail. We establish that IGFEM-based level set topology optimization generates correct topologies for well-known compliance minimization problems. Keywords Enriched finite element methods · Level sets · Topology optimization · XFEM/GFEM · IGFEM
1 Introduction The use of enriched finite element methods in topology optimization approaches is not new; the eXtended/Generalized Finite Element Method (X/GFEM) (Oden et al. 1998; Mo¨es et al. 1999; Mo¨es et al. 2003; Belytschko et al. 2009; Arag´on et al. 2010), for example, has been explored in this context. However, the Interface-enriched Generalized Finite Element Method (IGFEM) has been shown to have many advantages over X/GFEM (Soghrati et al. 2012a; van den Boom et al. 2019a). In this work, we extend IGFEM to be used in a level set–based topology optimization framework. Responsible Editor: Helder C. Rodrigues Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00158-020-02682-5) contains supplementary material, which is available to authorized users. A. M. Arag´on
[email protected] 1
Department of Precision, Microsystems Engineering (PME), Faculty of Mechanical, Maritime, Materials Engineering (3ME), Delft University of Technology (TU Delft), Mekelweg 2, 2628 CD, Delft, Netherlands
Topology optimization, first introduced by Bendsøe and Kikuchi (1988), has been widely used to obtain designs that are optimized for a certain functionality, e.g., minimum compliance. In the commonly used density-based methods, a continuous design variable that represents a material density is assigned to each element
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