Integrated topology and packaging optimization for multi-phase multi-component problems

Methods for integrated topology and packaging optimization are used for addressing coupled material and component distribution problems in lightweight systems design. Traditionally, these numerical tools incorporate component position design variables within standard topology optimization to efficiently embed objects within structural loadpaths. More recently, position-based variables have been replaced by component pseudo-densities, offering a new class of solution process referred to as component-existence models. This work presents an extended component-existence model with developments to the core theory, numerical methods, and best practices from initial implementations. Notably, the extended method developed here introduces multi-phase component modeling (solid-only and solid-void components) and generalizes the associated problem statement and numerical framework to support multiple geometries and packaging constraints. This includes aspects such as packaging symmetry and packaging sub-domains in general multi-component problems. Further enabling these capabilities are enhancements to the overall implementation, including incorporation of a commercial finite element analysis engine, new routines to smooth component pseudo-density discretization, and updates to manage component-to-component overlap avoidance. The resulting component-existence model demonstrates capabilities beyond previous implementations in various 3D single-phase, multi-phase, and multi-component problems and is discussed with respect to the key practical and numerical challenges within the field.