An Interface-Preserving Level Set Update Strategy for Topology Optimization of Mechanical Assemblies

Structural components in assemblies often require specific geometric features — such as cylindrical regions for joints — to function correctly. Standard topology optimization methods, however, struggle to impose geometric, feature-preserving constraints on selected boundary regions during shape updates. We propose a shape update strategy for level set-based topology optimization of mechanical assemblies that enables constrained shape updates along user-specified boundaries while allowing free-form updates elsewhere. The constrained regions are limited to affine motions such as translation, rotation, and scaling, providing greater control that is especially valuable in engineering design. This is particularly useful for multi-functional components in larger assemblies, where certain boundaries must retain primitive geometries and vary only within specified limits. For example, when a component must contain a cylindrical aperture to fit a pin of unknown radius, our method allows simultaneous optimization of the aperture’s location, orientation, and size, alongside the component’s overall topology. We extend the standard Hilbert space extension method by introducing its constrained variant which incorporates affine motion constraints into the velocity extension. The resulting velocity field satisfies descent direction requirements for the optimization while ensuring that all feature-preserving constraints are met. We demonstrate the method’s effectiveness on canonical structural problems with geometrically constrained boundaries.