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

TL;DR

This paper introduces a density-based topology optimization method for linear elasticity using cut finite elements, enabling flexible geometry representation and coupling with pre-existing structural parts through stable interface conditions.

Contribution

It develops a novel cut finite element approach with stabilization and coupling to nondesign regions, allowing complex geometries and integration with existing structures in topology optimization.

Findings

Stable coupling of design and nondesign regions using Nitsche's method.

Guarantees stability across the full density range, including traction-free limits.

Allows complex geometries on fixed background meshes with arbitrary cuts.

Abstract

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 represents 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.