Gradient-Based Multi-Component Topology Optimization for Manufacturability

Abstract

Topology optimization is a method where the distribution of materials within a design domain is optimized for a structural performance. Since the geometry is represented non-parametrically, it facilitates innovative designs through the exploration of arbitrary shapes. Due to its unconstrained exploration, however, topology optimization often generates impractical designs with features that prevent economical manufacturing, e.g., complex perimeters and many holes. Above all, existing topology optimization methods assume that the optimized structure will be made as a single piece.

However, structures are usually not monolithic (i.e., single-piece), but assemblies of multiple components, e.g., cars, airplanes, or even chairs. It is mainly because producing multiple components with simple geometries is often less expensive (i.e., better manufacturability) than producing a large single-piece part with complex geometries, even with the additional cost of assembly.

This dissertation discussed a topology optimization method for designing structures assembled from components, each built by a certain manufacturing process, termed the MTO. The prior art of MTO used discrete formulations solved by genetic algorithms. To overcome the high computational cost associated with non-gradient heuristic optimization, this dissertation proposed a continuously relaxed gradient-based formulation for MTO. The proposed formulation was demonstrated with three manufacturing processes.

For the sheet metal stamping process, by modeling stamping die cost manufacturing constraints and assuming resistant spot welding joints, the simultaneous optimization of base topology and component decomposition was, for the first time, attained using an efficient gradient-based optimization algorithm based on design sensitivities.

For the composite manufacturing process, a cube-to-simplex projection and penalization method was proposed to handle the membership unity requirement. With the multi-component concept, a unique structural design solution for economical composite manufacturing was achieved. The component-wise anisotropic material orientation design for topology optimization was presented without prescribing a set of alternative discrete angles as required by most existing material orientation methods.

For the additive manufacturing process, the MTO method enabled the design of additively manufactured structures larger than the printer's build volume. By modeling manufacturing constraints on the build volume limit and elimination of enclosed holes, the optimized structure was an assembly of multiple components, each produced by a powder bed additive manufacturing machine. The first reported 3D example of MTO was presented.