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We develop a density based topology optimization method for linear elasticitybased on the cut finite element method. More precisely, the design domain isdiscretized using cut finite elements which allow complicated geometry to berepresented on a structured fixed background mesh. The geometry of the designdomain is allowed to cut through the background mesh in an arbitrary way andcertain stabilization terms are added in the vicinity of the cut boundary,which guarantee stability of the method. Furthermore, in addition to standardDirichlet and Neumann conditions we consider interface conditions enablingcoupling of the design domain to parts of the structure for which the design isalready given. These given parts of the structure, called the nondesign domainregions, typically represents parts of the geometry provided by the designer.The nondesign domain regions may be discretized independently from the designdomains using for example parametric meshed finite elements or isogeometricanalysis. The interface and Dirichlet conditions are based on Nitsche's methodand are stable for the full range of density parameters. In particular weobtain a traction-free Neumann condition in the limit when the density tends tozero.

Cut Topology Optimization for Linear Elasticity with Coupling to Parametric Nondesign Domain Regions