## Continuum-Based Topology Optimization of Frames via Geometry Projection

One of the challenges of continuum-based topology optimization is that the resulting optimal topologies are often difficult to translate into manufacturable concepts. Optimal topologies typically exhibit members of varying cross section which cannot be easily manufactured. In the case of frames, one wishes to employ stock material, such as bars, tubes, I-beams, etc. Discrete topology optimization via the ground structure approach naturally handles this requirement, but it cannot incorporate multiaxial stress criteria since the analysis model is inherently one-dimensional; also, it cannot easily handle the situation when the members overlap, as would be the case if, e.g., one welds two bars one on top of each other. In our research we project the geometry of a finite set of bars of constant (in-plane) width onto the analysis grid, and penalize the (out-of-plane) thickness so that the optimizer can remove bars from the design space. The continuous and differentiable projection renders a density field, such as the one used in SIMP topology optimization. Hence, by using the chain rule we obtain sensitivities of the structural responses with respect to the bar design variables.

In collaboration with Daniel Tortorelli (University of Illinois at Urbana-Champaign).

Funding: *University of Connecticut*

## Design Optimization of Bone Scaffolds Fabricated via Micro-Robotic Deposition

Natural and synthetic bone graft materials, or scaffolds, are used in a range of orthopedic, cranio and maxillofacial applications to treat bone defects caused by trauma, disease, or congenital defects. In this project we employ a cellular solids model to establish closed-form relations between the manufacturing parameters and elastic properties of hydroxyapatite (HA) and β-tricalcium phosphate (β-TCP) scaffolds fabricated via micro-robotic deposition, which have been shown to enhance bone regeneration. The scaffolds consist of alternating layers of extruded rods, that upon sintering form a 3-d lattice. From a mechanical design point of view, the scaffold must be porous enough so as to favor bone growth inside the scaffold, and it must be strong enough so as to bear the loads imposed by the surrounding bone on the implant. The second part of our project consists of coupling the cellular solids model with a continuum-based structural optimization method in order to design patient-specific scaffold layouts (i.e. with varying rod orientation and separation).

Funding: *University of Connecticut*

## Topology Optimization of Welded Plate Structures

In this project we investigate a computational topology optimization method for the design exploration of welded fabrications. We aim to render optimal topologies that are made of distinct plate load paths (possibly with holes), thereby facilitating the translation of the optimal topology into a structural design concept that can be readily manufactured by welding of cut plates. This methodology will greatly decrease the time that designers have to spend producing a manufacturable fabrication out of the results of conventional topology optimization, which typically produces load paths of variable cross section that cannot be easily captured with plates.

Funding: *Caterpillar Inc.*