# Mixed projection- and density-based topology optimization with applications to structural assemblies

## TL;DR

This paper introduces a hybrid topology optimization method combining explicit geometric control with density-based flexibility, specifically tailored for optimizing structural assemblies and their interface shapes.

## Contribution

It presents a novel mixed projection- and density-based approach that unifies shape and topology optimization for complex structural assemblies.

## Key findings

- Effective optimization of assembly interfaces using geometric profiles.
- Ability to impose local constraints and material property variations.
- Numerical examples demonstrate design flexibility and complex shape manipulations.

## Abstract

In this paper we present a mixed projection- and density-based topology optimization approach. The aim is to combine the benefits of both parametrizations: the explicit geometric representation provides specific controls on certain design regions while the implicit density representation provides the ultimate design freedom elsewhere. This approach is particularly suited for structural assemblies, where the optimization of the structural topology is coupled with the optimization of the shape of the interface between the sub-components in a unified formulation. The interface between the assemblies is defined by a segmented profile made of linear geometric entities. The geometric coordinates of the nodes connecting the profile segments are used as shape variables in the problem, together with density variables as in conventional topology optimization. The variable profile is used to locally impose specific geometric constraints or to project particular material properties. Examples of the properties considered herein are a local volume constraint, a local maximum length scale control, a variable Young's modulus for the distributed solid material, and spatially variable minimum and maximum length scale. The resulting optimization approach is general and various geometric entities can be used. The potential for complex design manipulations is demonstrated through several numerical examples.