Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 350, Issue -, Pages 462-479Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2019.03.016
Keywords
Material distribution topology optimization; Design and nondesign domain regions; Cut finite element method
Funding
- Swedish Foundation for Strategic Research [AM13-0029]
- Swedish Research Council [2013-4708, 2017-03911, 2018-05262]
- Swedish Research Programme Essence
- EPSRC [EP/P01576X/1, EP/P012434/1]
- EPSRC [EP/P012434/1, EP/P01576X/1, EP/N026942/1] Funding Source: UKRI
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We develop a density based topology optimization method for linear elasticity based on the cut finite element method. More precisely, the design domain is discretized using cut finite elements which allow complicated geometry to be represented on a structured fixed background mesh. The geometry of the design domain is allowed to cut through the background mesh in an arbitrary way and certain stabilization terms are added in the vicinity of the cut boundary, which guarantee stability of the method. Furthermore, in addition to standard Dirichlet and Neumann conditions we consider interface conditions enabling coupling of the design domain to parts of the structure for which the design is already given. These given parts of the structure, called the nondesign domain regions, typically represent parts of the geometry provided by the designer. The nondesign domain regions may be discretized independently from the design domains using for example parametric meshed finite elements or isogeometric analysis. The interface and Dirichlet conditions are based on Nitsche's method and are stable for the full range of density parameters. In particular we obtain a traction-free Neumann condition in the limit when the density tends to zero. (C) 2019 Elsevier B.V. All rights reserved.
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